I am planing a trip from Cairns to Thursday Island
Unless you're in a chopper, plan to land at Horn Island.
I have done the trip between Cairns and Horn Island a couple of times, and I'd have to say that it is a beautiful part of Australia to fly.
As far as the weather goes, I would have to say that the dodgiest weather always seemed to be around the Lockhart River area.
If you're adventurous, there are strips all over the cape. Coen, Laura, Karumba, Kowanyama
Weipa, Bamaga, and once you are up in the Torres Strait, there are plenty of islands to go see. Coconut Island was probably my favourite, but there are quite a few others.
Read your forecast well, take plenty of fuel, a GPS would be handy, be especially vigilant with fuel drain checks after wet nights, and if the weather is marginal and you are in a VFR single, I would suggest staying on the ground.
Without knowing your experience level, it is hard to give specific advice, but it would be far wiser to go after the wet season.
Whatever you do decide, I hope you have a safe and enjoyable trip.
BW