You could get a Line of Credit loan on your half of the equity  in your name.  Then use this as a deposit for a completely new loan.
If you need your Dad to help you with the deposit he could take out his half of the equity as an LOC in his name and he could lend it to you. Or your DAD could go guarantor on his half of the equity so you can borrow the whole equity his share and yours as an LOC.

You may need to go to a solicitor so it can be explained to your Dad and yourself what the legal implications are on both of you to protect the banks from loss and for you to know the downfalls of such an arrangement.

What you need to think about ias well as having an emergency fund is a repair fund
What happens when a hot water system fails and you need to find $1500 in a hurry to fix it. Or a house gets run down and you need to spend $6000 to repair the house to get it into a rent-able state. A lot of property investors lower or aim for  the LVR figure of 60% because you could re-borrow the funds to cover an unexpected repair and the less hassle with getting finance due to the lower LVR figure.
The strategy you are using works well if you have massive capital growth due to the LVR figure decreasing as each property gains in value. It sounds like you have a problem with trying to grow your property portfolio to quickly rather than waiting for capital growth to make the LVR lower. It might be a good idea to concentrate on paying the lowest debt off while waiting for the capital growth to occur to a level where the income is more than the expenses.
A good example of what can happen with high Leverage is what has happened with Centro Properties in that the bank wants the funds paid back and Centro cannot find a lender due to the credit crisis.

Having had no full time job for three years has opened my eyes to the draw backs of negative gearing.

I am currently fixing up my rental property and have had no rent for the last three months as it has taken two months to fix the house up and it has been hard to find a tenant over Christmas.

Time frames are a consideration. In the time it takes to pay off one property you may have borrowed money and purchased 6 properties that have grown in value. However the interest costs and the holding costs and capital gains tax cut into the profit as you are forced to sell some properties at the end of the time period to bring down the debt. If you can pay off one property and then borrow money and buy another you can offset the income against the negative cash flow second property and the income of property one and two could be used to help pay off property two. Once you have property two paid off and one paid off you could borrow and buy property three and use the income from property one, two and three to pay off property three.
Property one is the hardest to pay off, Property two is a bit easier, property three is going to be easier, property four is going to be easier again. See the compounding effect if you return the income to building wealth.

Having had time to think about this question many properties also attracts State Land tax if the properties are in the same state of Australia.

Another problem is their rules change all the time and they don't tell you about them until you break a rule.
I was getting a part payment of parenting payment as I was looking after my two daughters and my wife worked .
The $60 a week was not worth the hassle of dealing with centrelink and their restrictive rules towards investing.
I now work part time and do not receive family B payment until after the tax return , so I won't get a bill if I earn too much.
I do not deal with Centrelink at all for the sake of my Sanity.

Kurt,
Have a Happy New Year.

You  need to talk with your accountant to get specific advise on setting up a Trust and whether it would be an advantage to have a company control the trust or an individual tax payer.
https://www.propertyinvesting.com/resources/products/11

William,
How I got started. Unlike you I did an apprenticeship and was good at saving. I saved up a deposit and when I meet my wife to be we decided to buy a house to live in. With her savings and mine plus our healthy employment record we purchased the house by walking into the real estate agents office. This is the hard part – getting past the real estate windows and actually talking with the real estate agent. We filled out the loan application with the real estate agent not the bank. Due to my wife's new career move we rented out this house and lived in a low rent house. This was 1995 and in 2001 I had a tax problem in that the house was making to much income so we decided to buy another house for $100,000 and while I was at University for the next three years I made the negative component of this investment from my savings and the rest from the rent. (this is an important point to note – once you have the loan it doesn't matter if you become unemployed as long as you can make the payments!)
When I finished university no one would employ me in a graduate position (A sore point) so I forecasted that my savings would run out in about 12 months so I put the second property on the market and sold it for $170,000.
I had to pay Austudy back as the $70,000 gain was deemed income and I had to pay capital gains tax.
I am currently looking at working as a bus driver as I have no intention of subjecting myself to the unrealistic tests and group tests of graduate recruitment programs of employers' out sourced recruitment agencies as they do not know what family friendly means and seem to be looking for the top 20% of graduates without caring what happens to the other 80% of graduates they keep passing over.

Only recently since April have I gained part time work as I have two three year old children to look after and mum works full time. I know how hard it is to borrow money in your situation as I have been in a non employment situation from 2001 to 2007.
Just recently I have scaled down and borrowed $30,000 and purchased shares as this is where my talents really are in making income.
Somewhere in this time frame I also did a property seminar run by Freeman Fox and have gained a lot of my knowledge.

So even though I only own one property I am sitting on about $150,000 equity, $50,000 in shares and $50,000 debt , so once I can work full time again I will scale up my investment level.

I forgot to mention also that our cars are paid in cash and are not brand new and also I do not own a LCD or Plasma TV and I do not borrow long term debt on my credit cards.

The investor meeting's in melbourne are in the following posting
https://www.propertyinvesting.com/forums/property-investing/general-property/4322700

This may help and I am certain consumer affairs or office of fair trading in your state would be able to direct you to the correct requirements

Consumer credit (Victoria) act 1995 see section 11
http://www.legislation.vic.gov.au/Domino/Web_Notes/LDMS/PubLawToday.nsf/a12f6f60fbd56800ca256de500201e54/153EC4DCA39B6B53CA2572E900127899/$FILE/95-41a025.pdf

I would assume each state would have a similar law act you would need to investigate

see
http://www.consumer.vic.gov.au/CA256EB5000644CE/page/Business+Licensing+&+Regulation-Credit+Providers?OpenDocument&1=30-Business+Licensing+%26+Regulation~&2=40-Credit+Providers~&3=~

http://www.fairtrading.nsw.gov.au

http://www.fairtrading.qld.gov.au

http://www.consumer.tas.gov.au/

From http://www.ASIC.gov.au web site
Our jurisdiction applies whether the lender is a bank or any other finance provider, such as a finance company, a credit union, a retailer or a firm of solicitors. It is not necessary that the lender is a firm that is licensed by us. Our credit jurisdiction is however limited to activities that take place in the context of "trade or commerce". We do not regulate loans between friends or family members, or other non-commercial arrangements.
Some credit providers may however need to be registered or licensed under relevant State legislation.

Who else regulates credit?
ASIC shares its new responsibility for credit regulation with the state and territory government's fair trading and business and consumer affairs agencies. These agencies have sole responsibility for the detailed regulation of consumer credit under the Uniform Consumer Credit Code [the UCCC].

If there is no oil there will be no war as every war machine runs on oil.
I read recently in the Age that Singapore was experimenting with a tidal power station and using the power generated to convert water into hydrogen to run their cars on.
I think that a certain country that can spend over a trillion dollars on one war will spend over a trillion dollars on developing an alternative fuel source to keep their war machines running.
If Fusion  (Hydrogen  – Sun  type reaction)  can be contained  as this is all that is preventing a  large scale  reactor  from being developed we will have more energy than all the fossil fuel already used from 1 cubic metre of  sea  water.
The heat is so hot that magnetic fields are trying to be developed to hold the reaction in.
Everything else melts.
http://physicsworld.com/cws/article/print/1258

I suspect oil companies have purchased an invention developed in 1979 that converts water to hydrogen with very little electrical power and uses it on demand rather than storing it. It was developed and mentioned in Electronics Australia in 1979.
 http://physicsworld.com/cws/article/print/1258

Probably you could inquire with your mortgage broker if you can have a list of the lending rules from the lenders they use most.
The main points are LVR, Income,security of employment and Credit Rating.