Yeah we were a bit worried about those, but according to the guys that ran the place it was fine up the top end of the beach away from the mouth. The road turns to gravel after Cape tribulation, but you can drive up as far as the Bloomfield river without a 4WD (I did it in a wicked camper - when it was dry, different story after rain I would imagine).
I just had a look and koala beach campground closed down! That sucks. There's also this place I've camped at, $15 a night and right on the beach just 10k further north:
www.capetribcamping.com.au/accommodation/unpowered-site (cant remember if it was windy or sheltered there)
As for Cooktown, there's nothing there. When you do find a "beach", you'll likely be the only person on there, let alone the only kiter. Enter the water at your peril.