My information is that all Australian residents and citizens only can buy existing properties.
In other words if you do not live in Australia or are not an expat, you can only buy a brand new property, be it house or apartment. You cannot buy anything “second hand”. You can buy land, but must build on it in a short period of time (not sure of the time frame). All applications must go through the Foreign Investment Review Board (FIRB), so they are they best people to check with for specific information.
NZ residents used to be able to just buy property here, but I believe the rules are changing to treat them the same as foreigners.
Lucy