good luck. it is possible, but a LOT of having to prove this and that, my friend was split from her partner, but in the same house, she moved into the babies room and had to prove to centerlink that they had infact split, i think she needed friends and family to verify all this as well as the huge amount of paper work and questions she was given. he has since moved out, but i know she was on single payments befor he actualy left.
good luck with it.