A few facts...
Only a very small percentage of Public Housing dwellings are 1 bedroom units.
Consequently, there is a HUGE percentage of 2 bedroom dwellings being occupied by single people.
Fact 2: It is NOT EASY to find a swap. Even with the super efficient Our House Swap website it can still be hard to find something that suits your needs.
Fact 3: It is virtually IMPOSSIBLE to get a transfer through the official channels - the average wait being 2 years.