A few points:
a) be resigned to driving if you want to do much in Melbourne..public transport is best described as "barely adequate" (certainly far below most European standards), and the city itself is geographically very large.
b) Toorak is certainly very plush and not far from the inner city, but there are many other suburbs that probably offer better value and are similarly pleasant and convenient (eg Armadale, Malvern, Kew, Hawthorn, Camberwell). It depends very much on just what sort of atmosphere you like best. Shop around!
c) MEL-SYD is just a one hour flight, quite survivable in Y.