In addition Tom's answer. If you are planning on returning to Australia with your dog then you are going to face strict quarantine restrictions that could preclude you from traveling with your dog anyway.
See Cats and Dogs returning to Australia from the Department of Agriculture and Resources. From that page:
When your cat or dog leaves Australia it immediately loses its
Australian health status. This means you might not be able to bring it
back to Australia at short notice. Please consider the information
below before exporting your cat or dog.
Cats and dogs can only be imported into Australia from certain
countries and, depending on the country, the pre-import preparation
time can be over six months. However, if you start preparations in
Australia before your cat or dog goes overseas, returning them to
Australia can be much simpler and quicker.
Also from that page (noting that the USA is considered a Group 3 country)
If there is any chance your dog or cat may visit a group 3 or a
non-approved country we recommend they have a rabies vaccination and
rabies neutralising antibody titre (RNAT) test before leaving
Australia. This will ensure they can return to Australia in the
shortest possible time. Rabies vaccinations last between one and three
years and you will need to check this validity with your veterinarian.
An RNAT test with an acceptable result (0.5IU/ml or more) is valid for
24 months from the date the blood was drawn.
Please note that you will need to maintain valid rabies vaccinations
and RNAT tests for the entire time your dog or cat is overseas. If you
don’t do this, your animal will have to meet the mandatory 180 day
waiting period overseas following an RNAT test if they have visited
any group 3 or non-approved countries.
So if you do not follow the rules then you dog will have to spend and additional 6 months in the US before you can even bring it back to Australia.
As a personal anecdote (but not related to your situation). I am planning on bringing two cats back to Australia in the next couple of years. To minimize the time they will spend in quarantine custody IN Australia, this will require rabies tests every month for 6 months. At which point once they are shipped to Australia they will still have to spend 1 month in quarantine.