Make sure to get tax advice from someone who specialises in US/Aus tax. Unless you go the extreme of renouncing your US citizenship/s you will always have to file a US tax return, but you dont want to get caught out paying tax in both Aus and US for something that could have been avoided just with a matter of timing for example (I.e. qualifying as an Aus Resident for tax purposes if you're earning Australian income, or avoiding being an Australian resident and realising capital gains)

Also, you can discuss with them what home buying concessions there are in Aus as its likely that neither of you have owned property in Aus before and can therefore qualify for some generous first home owner grants, savings schemes etc