Hi as long as you have a Vin # and bill of sale , or a reciept showing sellers details, purchase price and signed by them, you can apply for import approval in australia by the usual means.
The title will allow export out of USA. I dont see any reason why you would run into any issues in Australia, we dont need titles here at all, the Title in USA just allows you to be the owner and do what you want with it from there.
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