You can definitely "just turn up"... SpeedFortnight is about getting people together, in a location which is fast and nice (just remember to bring a wetsuit...).
That said, there are only so many beds to sleep in...
There is a caravan park, but space is very limited as it is now mostly for private campsites -> I haven't been there in years, so I dont have current info... you'd want to call "Sandy Point Caravan Park".
There are some cabins available from the shop "Sandy Point Cafe" (at one point they become unavailable, but I think that has been resolved). From memory they are about $75 per night. And there are some other places, such a Illuka cottages, etc.
Note that sharing a house for the two weeks, if often quite a bit cheaper at around $300 or so, for a bed, for the two weeks. Also worth noting is that night temp gets down to around 5deg, so caravan park is really cold....