I am very pleased that so many Perth MNers are coming out of the woodwork. One othread about living here with lots of rude comments and all sorts of people appear ;)
Seriously, on that thread, I just wanted to say that Perth has changed so enormously since we lived here in 02-04. The resources boom has made a city which had very little inward migration absolutely chockablock with people from Elsewhere. When we lived here before I couldn't go to the shops without at least one person asking where I was from (accent) but now you see and hear foreign accents constantly. It's changed the place for the better but as a result I wouldn't take the views of people who haven't been here recently all that seriously.
On where to live: Glasto and Nun make interesting points. Lots of people come to Perth wanting a great big house and great big block. Interestingly real estate ads here always give you the dimensions of the block and not the house, land size is a big thing here. Obviously for this to be affordable you have to be out of the city centre, but if it's what you want then you can get it, and it will be lovely! And indeed just like Ramsay St.
I think I am more like Nun in that my main criteria for living here was living within walking distance of school and shops, and to do that requires living in an inner suburb. For me, anything north of Floreat/Woodlands/Churchlands is too suburban and not my style (and that kind of comment does tend to intensely irritate those north of Floreat, but bear with me!). The older suburbs have central shopping strips with cafes and are lively and have more of a buzz. In the newer ones you get big blocks, big houses, usually huge numbers of kids, quiet, and still a strong comunity feeling but you have to drive absolutely everywhere, which I don't like. But I can see how others do.
So, if I were Mosman, I'd be looking at www.arta.com.au/wamaps/perth.html this very helpful map and given your MN name and what you liked in Syd considering the inner west suburbs that Nun mentioned (Cottesloe, Claremont, SUbiaco, Nedlands, Shenton Park etc). All have excellent public schools and you can see what you'd like. And seriously do PM me as I have visited most of these schools :) With your budget you should be fine especially if you are OK with starting in a flat. We rented a very acceptable 3 bed townhouse in Cottesloe for 700/week, which is a good price for that area.
Private schools in this area are all first rate but expensive!
Mosman Park might be a good place for a short term rental as it is well located.
Finally, and very important: some of the more oversubscribed schools may ask you to leave if you move out of catchment so take that in to consideration. And Sunny is right, try before you commit but it sounds like you'd do that.
Clearly we need a Perth meet up now!