I came across this site (relocation service) that has short term rentals, most furnished:
Moving to Melbourne: Accommodation Available in Melbourne
I don't know if its any good, but might be worth checking out. There are other relocation agencies that offer the same type of thing. So you could google "melbourne australia relocation service" and find a few. Good luck! We're hoping to have our visa by July-ish, and move in October, so are doing similar research (we have a 6mo baby, and a 7yo).