You should not have any issues as the vacancy rates are really high at the moment. Just get a print out of your bank statement (most recent) and you will be fine.
I rented out my apartment to a young couple (on working holiday visa) that just arrived in Perth. Also this place has been a rental for 7 years and during that time most of my tenants (80%) didn't have a job. Also most were all on visa of some sort and I have never had an issue. New arrivals are lot better tenants then locals in my opinion, especially if they are on a visa. I had only 1 tenant that was Australian and he was the only one who was late with rent.
Also, check out Gumtree for rentals, you are lot more likely to deal with owners which is a better way to go in my opinion.
Thanks sashamb we found a place and yes it wasn't that difficult as you said. Took only three days to get approved. !