In theory there’s a pilot shortage..in practice, the airlines are refusing to deal with it. There’s also a misguided notion that Australia trains superior pilots to anywhere in else in the world so by definition, that makes you inferior. You’re facing an uphill battle, however...if you have training experience and time on type you may find a home in Australia. QantasLink and Qantas will be a bridge too far though..that’s Astronaut territory. Your best bet is a second tier operator..you don’t have a Saab 340 rating by any chance? TRE even?
to be honest, if you’re really serious. Find one of the Aussie corporate jet operators that have chosen to leave their aircraft on the FAA (N) register. Especially if you have a global or gulfstream rating