Why would the existing populations of AU & NZ consent to becoming the subjects of some billionaire aristocracy? We're talking about millions of people formed into actual nation states with sizable and competent militaries. Not even the combined private security forces of 100 billionaires and 1,000 millionaires could take control and dominate something that large. Elon Musk isn't going to be able to wow them into submission with minisubs and beads.
I agree that setting up their own little city out in AU or NZ might be a better idea than the bunker. Maybe they can even take over a large section of the land mass.
In my opinion, it'll still be tough to fabricate all of the things that modern society depends on today. Maybe they can do it if they really put their minds to it, but I would be surprised.