I agree with Ben5 and Emmyloo. On the whole, Perth is a fantastic place to live.
We have moved internationally several times, have been in state and private schools etc. I really wanted Melbourne instead of Perth with the Australian move, because it does feel so much more like 'home' (European). But our time in Perth has been extremely happy.
Children are in local state school (and I love that there is no need for fencing, and they can just walk home - they are told to return to teacher if parent is not around, if that is the norm for them), while awaiting private school place. State school has been perfectly adequate, extending them where possible. There are elements of London school I preferred, but generally we are happy with their school, and so are they.
Health system is good. My DH takes train to work, it is air conditioned, regular, never delayed due to pollen, heat, sand, sharks, whatever. Best of all is the active lifestyle. DC are involved at life saving club etc, its so good to see hundreds of children running and swimming and having fun, instead of being behind closed doors. Of course they are lathered in sunblock, hats on etc.
That said, there is no denying that the cultural side of life is not much appreciated here (maybe we're in the wrong area for that?). When any show comes to Perth, you have to seize the moment! We've travelled to Asia a few times from here, as its so close, and airline sales make it quite affordable.
To Mosman I would say, the new arrivals that I know who have needed childcare places, have only managed by phoning and visiting every few days, generally making a nuisance of themselves. Good luck!