Benn: you have lots of options but at that time of year, it would be smart to book now to be assured of a spot. Most marinas have casual berths so it depends on what you are looking for off-marina. Do you want to be close to the city? on the North shore? Close to public transport? Also the rates are much better if you stay for 5 or 7 nights rather than for one or 2. Starting SE and circumnavigating: Rose Bay Marina offers casual berths in the centre of the Eastern suburbs. Then there's d'Albora at Rushcutters Bay (where we just spent 9 nights); it is an easy walk to train stations at Edgecliffe & Kings Cross. Lots of swell into the marina during the day which eases off at night, we paid $140/night. Then Birkenhead Point: it is building new 16m & 18m berths right now that should be available in October. Right at the foot of a big shopping complex for easy provisioning/hardware store/restaurants, ferry service and buses available right there and very protected from swell. Then Gladesville Bridge marina....good marina if somewhat subject to harbour traffic wash, but steep walk up to road above for bus access. Then d'Albora marina at Cabarita: would be a good choice for a boat your size, good access, excellent Thai place right at the marina, easy walk to buses everywhere and ferry services to Darling Harbour & the city, etc: I'd seriously consider that. Then going over to North side, if you have a car/going to hire one consider Woolwich Marina. Then try Royal Sydney Yacht Squadron MIGHT have a casual berth for you at Kirribilli: fabulous location and makes visiting the PM & GG easy. Couple of other marinas in Mosman/Neutral Bay but unlikely to have berths big enough for you and manoeuvring room very tight. Then around into Middle Harbour, d'Albora at The Spit is a big marina & almost certain to have a berth that would suit you. Buses at doorstop to Manly and the city. Fergusson's is adjacent and would be an alternate. In Middle Harbour proper there are good marinas at Cammeray & Roseville; both are steep up to the road above with limited public transport access. My top 4 would be Rushcutters Bay; Birkenhead Point, Cabarita; The Spit in no particular order.
Cheapest fuel in Sydney Harbour is at White Bay (Bailey's Fuels).
I've assumed that by Sydney you mean Port Jackson proper and that you're not interested in Pittwater or Cowan...that's a whole 'nother story.
Does Mooloolaba marina where you are now have any reciprocal arrangements with marinas in Sydney?