I moved to Adelaide 3 weeks ago, and I have found that I have settled really fast. Before arriving I sorted out a studio flat rental in the CBD for the first week, and then hospital staff accommodation for after that through work... managed to time it so that I never moved into the staff accommodation building!
I managed to find my fully furnished rental within 4 days of arriving and secured it that day by offering to sign a 12 month lease, rather than the 6 months they asked for. There aren't huge numbers of furnished place available but it's definitely do-able, and I had a smallish budget of $300 per week and got a 2 bed unit for that right on the tramline into town. Moved into my place 6 days after arriving, and its been reasonably easy to get everything sorted. My place even has all the utensils and linen, made it even easier to get settled in without having to go on a mad Ikea dash in my first week!
As everyone has said www.pomsinadelaide.com has been a great source of information, I highly recommend it.