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hi robert,
im sure you will be able to get a job in australia, it may be getting the work permit that will be your only hurdle.
But in saying that if your degree/experience is recognised with the australian standards, you should be able to obtain a permit easily, either by being sponsored by an employee or a by opting to get a skilled migrant permit. link to visa's
I just done a quick search for a job and this is what came up:
Your job search found 290 Jobs matching "electrical engineering" in Melbourne, VIC.
So, im sure you will have the option to be a little picky and choice the right job in any state 
heres some job search sites
seek
career one
my career
As for the cost of living, if you choose to live in the heart of the city you will be paying top $$$ move out a few suburbs and the prices will come down, i know we have a few auta's who work in real estate and they may be able to help you more with this subject 
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