The university also owns two blocks of self-catered apartments. The Barker apartments are on campus, but I'm pretty sure that all the places for this year are taken, but you may have some luck with the Mulwaree apartments. Mulwaree is about a 15 minute walk from the uni, very close to the Randwick shops, and convenient to get in to the city from. The apartments have five bedrooms each and come furnished with things like a bed and a sofa.
Most of the rooms for this year have been offered, but if you ring the Housing Office on 93854985 and ask to speak to Graham Jordan, he may be able to help you. If not, the housing office can help you to find temporary accommodation until you're able to find something permanent.
Good Luck,
ellie