Try contacting the Australian Embassy in Washington, or the local Australian
Consulate if you live in one of the major cities. They should be able to help you or at least inform you of which Australian government entity is responsible or regulates the import of exotic pets. Talk to as many people as you can asking the same things over and over again. You will find that most everyone will have little pieces of information and eventually you will find someone that will know what they are talking about and puts all the pieces together, at least that was my case.
As someone else suggested also look into the airlines, you will find that most do not accept pets and the one that did only allowed one pet per passenger (UNITED). I had to buy my best friend a roundtrip ticket so that I could travel with both of my fids (CAG & DYH) in the cabin. My poor GSD and cat had to travel cargo with a lay-over in Chicago, I still think of what a nightmare it must have been for those two.
There is the CITIES permit (takes about two months) and that has to be signed off by the Department of Fish and Wildlife the day of your departure (my local agent met me at the check-in counter - SFO). Not all airports have these facilities, there will be a list of authorized exit ports which to choose from on your CITIES permit.
In my case each bird had to be accompanied with a couple of U.S Origin
Health Certificate (VS From 17-140) issued by a veterinarian authorized by the US Department of Agriculture (USDA) and endorsed by a Veterinary
Services (VS) veterinarian, usually this involves a trip to the State
Capital. The certificate could not be more than 7 days old and I had to meet all sorts of requirements. Quarantine (did at home), tests for Avian
Influenza, Newcastle Disease, Salmonellosis and have a letter from the VS stating that the birds came from an area free of the West Nile Virus. My birds required to be either banded or tattooed while my local guy with the
USDA preferred the use of microchips. Tuko was banded since he was a baby so he only got a microchip while Birt had to get both banded and microchiped and to this day he holds a grudge. It took me 6 months and literally thousands of dollars to make all this happen but eventually it did.
Everybody has different laws and although the requirements that you must meet might not be the same as the ones I had to meet I hope some of this information is useful to you.