P&D,
It'll be warmer with high humidity up Cairns way in December seeing as that is either on the cusp on or right in the wet season depending on whether there is an early arrival or not - yearly variations!
But if that is the plan, as they say - you'll just have to suck it up, but at least if it rains it will not be cold.
Go and stay at
www.capetribbeach.com.au , great little place right in midst of rainforest and right at Cape Tribulation, and to escpe the humidity, the Atherton tablelands could offer some respite -
www.onthewallaby.com being a well regarded tablelands active tour mob and they have a hostel up in the tablelands at Yungaburra and the classical old timber (some claim to largest) pub there ought to be worth having a drink at, the Curtain Fig Tree not being too far away.
If you want a cheap island trip, think about Fitzroy Island for which you can take a ferry type boat ride and though the resort out there is being remodelled, there is a camping area where you may still be able to pitch a tent - get a cheap tent from a Kmart or BigW store, and as you move down the coast you will find plenty of great holiday caravan park/camping grounds that are often right on the beach and can be cheaper than hostels.
You'll find it humid nearly all the way to Sydney, but beachside you get a bit of relief, Cairns itself having no immediately close real beaches and until you get down to the Sunshine Coast, beware swimming at ocean locations for there are Box Jelly fish and other marine stingers that can be fatal.
If you're after some cheap travel, have a look at
www.standbycars.com.au and the hot deals re doing a campervan relocation - can be extra cheap and if needing a few more days than what is allowed, a few extra can be obtained at a discount rate depending on required delivery date - but that way it is easy to stop just about anywhere overnight for free - there being many legitimate free stopping places and then if at a quieter smaller town, just be discreet and away in morning and you'll usually have no problems.
If you were planning on being in Sydney between Xmas and NY, I suspect you may have problems getting accomodation for it could be just about all booked out, even by now.