If the US used our system, Trump could never have been elected; he would first have to be elected to a seat in parliament in his own right, and THEN be voted leader of his party
FWIW, almost no one elected as US President would have qualifed in the Aussie system. I believe #11 Polk was Speaker of the House on election day; and #36 LBJ had been a Senate Majority Leader, but not when he was elected President. I suspect Henry Clay might have been a party leader at least one of the five times he lost in Presidential elections.
The system you describe requires that only those who have steeped the longest in the waters of corruption can become the chief executive. I find little comfort in that.
I confess that I am just learning the Aussie politics from your post, a few internet searches you caused me to make, (and the occasional fact I pick from watching reruns of The Chase). So, you can correct me if this is wrong. You have a monarch, the monarch appoints the governor general, and the governor general can remove the prime minister, and remove the members of Parliament? And this actually happened? And you don't think the queen is running things?