Hi From Australia
whilst I am not a USA citizen, I have met meany people who have purchased Australian registered vehicles here who are tourists.
A lot of the European backpackers do it most just use the address of the hostel they are staying at for this.
If you want to make it a more permanent arrangement then a number of groups can sell you a forwarding mailbox that allows you to have an address.
1 word of caution though every state and territory in Australia has its own rules on vehicle registration. Some require that an annual inspection be carried out some like WA were I am from don't.
Generally we are probably quite a relaxed country to get things done in with exception of importing things, guns and knives!!! oh scratch that most of the things that one can kill another with except cars we are hard to deal with.
if you have some specific questions just drop me a private message and if I know the answers I will try and help
regards
Carts from WA