I'll probably go into very great detail about it at some point, but the answer is "nowhere near as well as people think".
Australia is significantly more urbanised and centralised than the US is which means that a lot of the cultural conservatism in the US doesn't apply anywhere near as much. It's also far less religious, and a lot of the religious voters here aren't Anglo.
Sure there'd be places where Republicans could do well in Australia. But it certainly wouldn't be anywhere near enough to gain a majority of seats.
I don’t think anyone thinks the GOP could win more than 45% of the PV in Australia on a good night. I assume that the only red state is Queensland and maybe slight red WA?