Chances are that the answer is no. UNless you search in the place where you bought the first one, and you also attend to some business regarding that property while you are there….
Others may have different, better opinions than mine []
Travel expenses to purchase a property are kept in the capital area. If you sell the property in the future, the travel expense will be deducted from your capital gains along with legal costs and stamp duty.
If you want to get out of a hole, first stop digging.
bennido,
Travelling costs to purchase a property are a capital expense so not deductible against the rent. Even though they are capital costs they are not included in the cost base on sale either, because they do not fit within the definition of the 5 elements that make up the cost base as per the legislation. This opinion is covered by the ATO in ID 2003/771.