...and many would enjoy living in your great country. But my understanding is that the Australian government doesn't allow non-citizens to hold a job.
Is that true?
(I was told this by an American who married an Aussie Sheila. He wanted to live there a few years, but wasn't allowed to work, so they came to the U.S.)
Not true. Like other foreign coutries with a socialized medical system, they are always looking for physicians, nurses, etc. Arrangements can be made if your qualifications are right.
Certain categories of visitors can work, but permanent residency pretty much guarantees it.