Hi Shani,
Most rental agents have a points system and you have to provide documents worth so many points. A print out of our Aussie bank account ledger, my aussie drivers licence and UK passport secured our rental. I did bring 3 months of bank statements, utility bills and proof of mortgage payments to show why we didn't have any rental references (some real estate places ask for this too!) just in case but it wasn't needed. I think it's better to have too much rather than not enough though, just to be on the safe side.
Felicity
