I'm from Brisbane too. I'm yet to dive Flinder's Reef. There are one or two shore dives you can do around Brisbane but mostly the best dives require a boat. The two shore dives I've done are at the Tweed River (a drift dive - would do again) and at Noosa (the Boiling Pot - and would DEFINITELY not do it again...freaking scary getting in over the rocks, shallow dive with a very strong surge).
North Stradbroke Island has quite a few dive sites around it, as does Moreton Island. Apart from these two areas, I'm not sure of many other dive sites around the Brisbane area. Straddie has a dive shop, but not aware of any on Moreton Island.
I get my tanks filled at Allways Diving (Moorooka). They're a small dive shop and they know everyone by name - a good vibe. They also have some pretty good prices for dive gear.
Mooloolaba and Noosa are my main dive sites at the moment. The HMAS Brisbane (Mooloolaba) is a fantastic dive - lots of fish and you can swim through it too. You can get a $20 permit for the HMAS if you have friends with boats. Otherwise it'll cost you around $150-200. Mooloolaba also has the Inner and Outer Gneerings, and Old Woman Island. These are moderately shallow dives. Old Woman Island tends to have a fair bit of surge and strong currents so best done in good weather. Noosa has The Pinnacles and The Caves (at Laguna Bay). Some of these sites are not so easily found so if you need the GPS co-ordinates, let me know. There are also 2 dive shops in Mooloolaba and 1 or 2 at Noosa.
I'd like to do the shore dive at Caloundra, but so far have only heard word of mouth info, nothing solid from the internet. I'm sure it exists, tho!
Gold Coast has some good dive sites too. There's Fido's Reef, Shag Rock, Cook Island and I'm sure there's plenty more that I haven't been to. Kirra dive has a good website and are probably a good dive shop to go with.
Julian Rocks at Byron is also a good dive, and there are plenty of dive shops down there that go out there. Be warned - I believe that most dive shops launch the boat from the beach, so it's a straight-out bar crossing.
I'm yet to do Wolf Rock at Tincan Bay but hear it's a good (and sometimes shark-filled) dive.
I hope this helps!