great place to live. I was a raft guide on the tully river a couple years ago, the tully and baron river both of which are north of you are hydro controlled so they run year round but as you are heading into the wet season this is when things start getting fun. The other river right between them is the north johnston this I did not get a chance to run because of the difficulty in getting there and it is a multi day trip the comercial companies helicopter everything in.
The tully is grade 4 very fun, mainly a technical run I gage it somewhere between the upper yough and upper gauley but I have seen it as big as grand canyon when the cyclones come. To hook up with boaters head up to mission beach that is where a bunch of the guides live, try Scotty's backpackers and pub in wongaling or the mission beach resort on wednesday they almost always have some guides hanging out there.
The only place to hire a kayak is up in Cairns, I don't remember the name of the shop.
The baron river is north of Cairns maybe 1/2 hour drive this is a much easier river to gain access to and find people to paddle with. While you are up there I highly recomend the sky ride up the valley past baron falls it is pretty cool.
The 2 river companies there are R N R rafting and Raging Thunder both of which are based in Cairns but have booking agents in mission beach and I am sure other towns at the backpackers.
There are more rivers in Aus but down the coast and I am not familiar with them.
Good Luck and watch out for all the little creatures there that will kill you