I can only comment on medical school rankings. Medicine is the opposite of Business in terms of reptuation vs licensing. In Business, its all about your business school rep. A top business school grad can potentially work anywhere in the world based on his school's rep rather than whether or not its been accredited by the world MBA bodies. Whereas a top medical school grad can work wherever he/she's licensed. Being a Cambridge medical grad won't entitle you to skip the USMLEs.
However, if you do go to a world famous school and realistically, this would probably only include Oxbridge and possibly some of the other top medical schools, this might help you slightly. It won't make a big difference and you certainly can't use it as a crutch.
Either way. If you go to Australia, make sure you are willing to put in the hard work and effort to apply back to the US. You might get to stay in Australia, but the chances are variable (your future is in the hands of politicians not yourself, do you want to bet on the whims of politicians?). Since you are a US citizen, it might make it easier to return and u don't have to believe all the hype about no residency spots.
They will continue to take very qualified high USMLE scoring IMGs in primary care fields. No you won't have a shot at Mass Gen, NY Pres or Cedars Sinai. You also probably won't have a shot at competitive specialties, but if you want something in primary care, don't mind hard work, then yes pursue medical education abroad.