There seems to be some confusion:
the ONLY way to get to the dunes is through the DNR controlled gates. After these gates is a huge parking lot, where you can bring your camper, truck, trailer, or whatever. The only way to get into this parking lot is to have a state parks sticker on your vehicle. These cost $24 a year, or $4 a day. This parking lot is accessible directly from public roads, so that means that no off-road vehicles can drive into the parking lot - they must be towed or trailered in.
once in the parking lot, you can drive you quad to a DNR station where they check for spark arrestors (and once in a while sound), then you go into the enterance ramp to the dunes. Thats all there is to it
no one that i know of did any booking, so I think you are on your own unless someone who is camping fr sure steps up
Ray