I hate to rain on your parade BUT....
Unless you have a skill that Australia really, really needs (like nuclear power station design) you have a snowball’s chance in hell of being able to secure a work visa here for a very long time. We have to get our own unemployed off the State tit as soon as we can, even if that means forcing people to go fruit picking.
Add the fact that GA is in terminal decline, and I fail to see any flying opportunities that won’t be snapped up by a few sufficiently wealthy locals who will fly for free or may even pay operators just to build hours.
As for flight schools, if you really must, a few will take your money, promise a job at the end of your training and deliver the licence, but when you are done the job won’t be available. Ex airline pilots are taking basic instructor jobs just to stay in the game.
A few other schools will take your money, promise the earth and collapse before your training is complete.
Caveat emptor.