Hi Cinderella,
I just want to share my experience in Melbourne CBD. When my wife and I came here in Australia. We stayed in a studio unit in 268 Flinders Street (home@flinders). It cost us around $300 per week. Their 2Br cost around $450. It is fully furnished.
You can also look for an NRAS housing (housing catered for students). This is usually bigger and nicer than traditional units in CBD. It is also cheaper by 30%. You can get a fully furnished 2Br apartment for $400/week.
Just want to share this info with you. Hope you can find your flatmate asap. Good luck.