I would probably start with the relevant building association. Here in Brisbane its the QBCC (Queensland Building and Construction Commission), other states will have their own association with similar laws and regulations. They’ll be able to get you on the right path.
Would probably go something like, have your current elevator installation license recognised by proof of knowledge and works completed. Then, an interview here and there maybe and some light reading to bring you up to Australian standards, if you aren’t already. Maybe some kind of fee somewhere for something and probably some other thing too for the sake of it. After that you should be right. Once they see you can indeed install elevators safely, they’ll set you loose and you’ll become like the rest of us.