hey v8 ranch,
i would recommend you start on the gold coast and work your way up the queensland coastline, the weather in queensland is pretty good all year round (much warmer than melbourne anyway) and there are lots of things to see including the late steven Irwin's zoo (rip) Australia Zoo, the theme parks, Movie World, Sea World, Dream World, Wet and Wild World, all great for the kids. You also have the sunshine coast (Noosa, Mooloolaba) I was in port douglas last year and noticed a lot of americans holidaying. A drive from gold coast to port douglas is approx. 2000km and plenty to see. There are alot of great inland drives in QLD also, you dont have to stick to the coast
As for an airport, you'll probably have to fly into Sydney, then catch a domestic flight to Gold Coast (Coolangatta airport).
If this doesnt sound like you, Melbourne is also a great city to see, just try and make it between november and april so you get good weather.
Good Luck with your decision
try this website also
www.tq.com.au