We're settling in great, thanks. We have girls aged 2 and 5 and they're loving it. They just see it as one huge adventure at this age. We worried about them lots at first - but then we figured we were just "worrying on their behalf" and their child-like attitude to everything actually becomes a source of strength!
Don't worry too much about getting here 'in time to register' - in our experience things can be pretty informal school-wise (and why not I say!) and you might find Principals quite happily saying "she can start next week", really - it's that simple.
You will need an address to enrol a child though - some schools we toured asked for a rental agreement as proof we were in their zone, others didn't seem too fussed - but you won't know that until crunch time.
As for Seacliff/Brighton/Kingston/Marino - I can't imagine driving into the city. Parking is fantastically expensive and the roads can get snarled up in rush hour - like anywhere. However, the train takes 21 minutes (26 minutes if it isn't an express service) and costs $3.09 each way (a 10 trip pass costs $30.90 and you stamp it each time you travel). Trains are frequent and (so far) pretty reliable. There are level crossings everywhere though (hardly any bridges) which is great for trains but bad for cars.
Any other help/advice needed just let me know.