I just think it would be so hard to do that. Their system is just so different. I'm not even sure what the path to become a doc is in Australia, what the relevant mental health law is, and what the brand names of the meds are. I'm sure none of that is insurmountable. But I think I'd rather just go on vacation.
The system is different, but for the most part, it's actually a much easier system from the doctor's perspective. Everybody has the same basic insurance (although some people have secondary insurance to top it up), which makes billing and prescribing much easier. You know exactly how much you'll get paid for everything. Billing codes are much simpler. All drugs are covered by the public health system (with a copay). The inpatient psych units are nicer. Most of the meds have the same brand names, except for some older drugs. Strangely, a couple of meds have different generic names (really just two drugs - acetaminophen is paracetamol and albuterol is salbutamol). Social services are more comprehensive. Addiction resources are more accessible. You don't have as many trainwreck patients because everybody has access to preventive care and early treatment.
Cultures are pretty similar. The hardest thing would be learning some of the Australian colloquialisms, but Australians understand American English pretty well (they all watch American TV), so they can easily translate for you.
Overall, transitioning to Australia will probably be easier than transitioning to a different health system in the US.
Also, while I think that Australia is nice for a vacation, there's as certain character to Australian culture that's really nice to experience if you can spend an extended period of time there and actually work there. Everybody is much more relaxed.
As far as I know it's only General Practitioners that are subject to the 10 year moratorium where they have to practice in areas of need for that period of time, and don't have the option to necessarily choose where they practice. Otherwise all IMGs (International Medical Graduates) have to under take certain pathways to registration depending on things like their training, and what overseas institute they studied at. My understanding is IMGs are given provisional registration with the medical board of Australia until they've completed whatever pathway is most relevant to them, at which point they can apply for full registration (no restrictions on practice). The specialist pathway is slightly different and that is where some restrictions come into place, but that also depends on what you're actually planning to do. If you're looking for Specialist recognition then as long as you have completed the requirements to be admitted as a Fellow of an accredited college you can apply for full Specialist registration.
The moratorium is for all specialties, but doesn't apply to psychiatrists because the whole country is an area of need. It becomes more relevant for GPs because their training is short and there aren't as many areas of need, so they have to travel somewhere else to fill the moratorium. Other specialists spend a lot more time in training (the training there is more gradual - it can last 7-8 years for most specialties, but the hours/pay are better than they are here, so it doesn't feel like residency), and I think that counts towards the moratorium, so it's not as hard to fill the requirements.
But that mostly applies to people who aren't fully-trained specialists in countries that are considered to have equivalent training (including the US). If you fall into that group (as most of us do), each specialty board has its own requirements.