I don't have any information about Australia, and I can tell you that I found my trainer through a lot of luck, but I can also tell you that trainers like this do exist, because the one I work with meets basically all your criteria. For me, I signed up for a free session with a trainer at my gym and had an absolutely horrible experience. I complained to the fitness manager. She gave me another session with herself, then set me up with someone she thought would be a better fit. That person's been my trainer since February; she left the gym because of its hard-sell attitude (she actually cares and listens when her trainees tell her they can't afford to increase their number of sessions) and now trains me at the gym at my apartment complex for less than she was charging at the other gym.

I would think that any trainer worth his or her salt would give you a free session to try them out and see if they're a good fit. Good luck!