Hi KJA,
Good luck with your search. In my opinion of searching for electronics design jobs in Australia is that the main bulk of design tools is Autocad. The main thrust for engineering in Aus right now is mining and railway. So if you are good at PLC's and Autocad, you are on to a winner. There is not a huge market for high end electronics.
But a try for you is black magic systems in Melbourne.
Hope it helps and good luck. Australia is a fantastic place to live, if you can get a job, and you won't get one from here, you have to go out there. Have a holiday, and go round all the agencies, get offered a job then go.
Monster munch.