There are several backpackers and a YHA in the city. Besides that there's a Formule1 hotel near the airport. A room will cost for both of you A$ 59 currently. Check for Perth accomodation on the web.
By the way, from the international airport there's no public transport. The shuttle bus is private and costs as far as I know A$ 12 and brings you directly to hotels and bachpackers.
Only when we pause to wonder
do we go beyond the limits of our little lives.