First, finish at least 2 years post-grad training in the US.
Then you have options for how/when to come:
A) After the two years, you can get your full medical registration here fast-tracked (via the Competent Authority Pathway), which means no AMC exams, but you'd still need a year of supervision before getting registration, which means a year here before you can apply for Permanent Residency (PR), needed in order to start training in most specialty training colleges here. While working towards registration, you're pretty much restricted to being an RMO (house officer) in a larger public hospital. After getting registration, you can continue as a house officer or can also locum while waiting on getting your PR (or apply to a training college that doesn't require PR, such as ACRRM or rural GP training -- though doublecheck as they keep changing the damn requirement). PR can take 6mos to 2yrs to get after registration, though from what I've seen and done, if you go through the state sponsorship route is on the shorter end of that range.
http://www.amc.org.au/index.php/ass/apo/cap
B) Nearly complete your specialist training, and apply via the Specialists-in-training pathway, which if you can get a training position offer allows you to fast-track things even more. But you can only do up to two years of specialty training through this method.
http://www.amc.org.au/index.php/ass/apo/spp/sitpsv
C) Complete your postgrad training in the US, then apply through the Specialty Training route, through which your specialty training is assessed, skipping the AMC supervision requirement but normally requires examination and/or supervision for 1+ years under the specialty college. The process varies by specialty. Generally speaking, to do this you need to have been offered a job in an Area of Need (essentially, a job that at the state level has been determined to be difficult to fill -- from easy to find, if you're a family practitioner, to extremely difficult to find, for some specialties).
http://www.amc.org.au/index.php/ass/apo/spp/spfr
http://www.amc.org.au/index.php/ass/apo/spp/aonsp
D) If you are training/trained as a rural generalist (or family practitioner), there is yet another process, presumably slightly easier than for C), but I do not know the specific differences. This is done through the rural GP college here (ACRRM):
http://www.acrrm.org.au/img-program
For any of the above, you would fall under the Moratorium, which requires you to work in an Area of Need for 5-10 years (depending on how rural you are) after the date at which you got full medical registration through the AMC. Training time is excepted from that requirement.
