Queensland / northern NSW is an excellant choice, although a stop in Sydney and the Blue Mountains (including Katoomba and the Jenolan Caves) are well worth a visit.
Brisbane is okay, but it is really a gateway to other places - you can pretty much hit all your list within an hour or two drive of Brisbane.
From about an hour north of Brisbane is the Sunshine Coast which has some plenty of nice camping / hiking areas, and beaches. Do look just inland as well, at places like Maleny and Montville. If you are a Steve Irwin fan, his zoo (Australia Zoo) sits near the Glasshouse Mountains. From about an hour south of Brisbane is the Gold Coast which has a lot of beaches and a lot of touristy things like the amusement parks (Sea, Movie and Dream Worlds amongst others). For camping / hiking however I would suggest going inland to the Natural Bridge or Lamington National Park (you can stay at O'Reilly's or Binna Burra). From Brisbane it takes about 1 3/4 - 2 hours to drive up to either O'Reilly's or Binna Burra (about 1/2 on highway and the other half up thinner mountain roads). There are some diving spots off both places or in Moreton Bay too, such as Moreton Island (out from Brisbane), and mostly are wrecks.
In northern NSW you have Mt Warning on land and down to Byron Bay are is great for water based activities.
Heading up the Queensland coast, Fraser Island is brilliant. Up the coast from there, there are plenty of islands and (Great Barrier) Reef such as the Whitsunday Island chain, Heron, Dunk, Lady Elliot and a whole raft of others...
Cairns is another gateway spot to the reef as well as rainforest (Kuranda is a great day trip, but there are longer stops too). Keep an eye out the back of Cairns to the Atherton Tablelands to such places as the lave tubes out there (volcanos erupted hundreds of thousands or millions of years ago and the outer side of the lava hardened but the inside has gone leaving tubes)