Sunny, i went to school in Aust and have a september b'day, turned 13 in Sept year 7 and that was completely normal...was one of the older ones but by no means the oldest. Your DS would be absolutely fine and there will be kids older than him.
My younger bro is dyslexic and went to school \link{http://www.sacs.nsw.edu.au\here} and my parents were very happy with the help he got. Not cheap but not one of the dearest either. Its right in the middle of the City and not particularly strong in sports, so may not suit your DS. Friendly school though.
I lived on the north shore and loved it - we will take the family back there in a few years to live. As someone else said, being on the trainline is good, or at a wharf (if you can afford to be that close to the harbour - lovely!) There are some good bus routes where your DH could get a bus straight into the CBD, but agree you and kids will need a car for sure.
Some suburbs that are lovely but expensive: Mosman (especially near balmoral beach), Cremorne, Neutral Bay, ...not on the train line but near ferries (depending on where in the suburb you are...busses normaly run to the wharfs). Waverton, Crows Nest, St Leonards are on the train and nice, but not as green as are near the North Sydney CBD...Artarmon, Chatswood, Lane Cove, Roseville are all lovely, good transport, slightly cheaper (as further from city) than Mosman etc, and Chatswood is only about 20 mins on the train from City.
Cheaper again but still lovely and green are Frenches Forrest, Belrose, Davidson...these are a fair bit further out but still on the North Shore so generally good schools, fascilities, parks etc. Not sure about transport here though.
\link{http://www.sydneybuses.info/\buses}
\link{http://www.cityrail.nsw.gov.au/\trains}
Let me know if you have specific Qs about suburbs, schools etc...might not know but might as I'm a Sydneysider!