Here's whats i'd do:
Arrive into Sydney
2 Nights - Sydney - Opera House, Bondi Beach, Harbour Bridge, Shopping
2 Nights - Melbourne - Arts, Music, Shopping, Crown Ent (Casino), Eureka Skydeck 88
2 Nights - Cairns, Port Douglas - Barrier Reef, Snorkeling
2 Nights - Gold Coast/ Brisbane - Theme Parks, Beaches, Shopping, Clubs, Q1,
The Valley (Music & Markets), Surfers Paradise, Jupiters Casino
Fly out of Brisbane (its only 1hours drive between GC and Brisbane)
I like your itinerary, but I'm going to suggest an alternative one.
As a tourist, I'd avoid going into cities and staying there for long. There's no point. Sydney isn't really a culturally rich place, and if you come to Australia just to walk around the cities, you're really wasting the little time you have in Oz.

Enjoy the scenery, the sun, and the beaches.
Itinerary:
1 days: Sydney - Opera House, Bridge (possibly do the $200 Bridgeclimb), Darling Harbour, Botanical Gardens, The Rocks market, Queen Victoria Building (QVB....it's an old, fancy shopping mall), ferry ride to Manly (Beach). All of this is easily do-able in 1 day. In fact, the Opera House, Bridge, and The Rocks Market are within a 0.5 km radius.
2 days: Gold Coast. Spend one day bumming around the beaches at Surfer's Paradise, and another day at one of the theme parks.
1 day: Brisbane, but only go there so that you can go with a tour company that'll take you to Morton Island, one of the largest sand dune islands in the world. Frasier Island is the biggest, and is definitely an alternative (although it's a bit further from Brisbane). Don't bother spending time in Brisbane. While I'm sure there's stuff to do, it'll feel like a wasted day. Trust me, I'm Canadian, and I've been to Brisbane twice, including my trip 1.5 months ago.
3 days: Go to Cairns, and do as much as you can. Go to some small island somewhere and chill out, go snorkelling, do some diving at the Great Barrier Reef, and possibly go to "Daintree Rain Forest" for one day.
1 day: Back to Sydney. I'm assuming you're flying home from here, right? Spend a relaxing day just hanging around here. The IMAX at Darling Harbour has the largest screen in the world. Absolutely incredible experience!! I highly recommend "Deep Sea 3D" if it's still playing there.
