I don't remember any caravan parks out there! You can probably pitch a tent at the roadhouses...but even they're a l-o-n-g way apart. Make sure you get a map and plan out when/where you get fuel.
I do remember how awesome it was to just drive off the highway a few hundred metres and pull up behind bushes for some free camping, sometimes with views over the cliffs (although, seriously don;t get too close to the edge!). If you can get far enough away from the big truck noises, there's no one else out there to annoy you with loud music or a generator running all night. We had a fire sometimes with wood gathered from the surrounding area. But always left the place clean and took our rubbish with us. almost 8 years ago
The drive across the Nullabor is a breeze. Lots of Roadhouses along the way. Cheap showers, Roadhouse food, and petrol. Most people stay at a Roadhouse as the over night cost is not much at all. Why free camp when it is a great way to meet all types of fellow travellers and share a yarn or two. Also, why not support the people who live is such a remote part of Australia. Hubby and I LOVED our trip across, will you. almost 8 years ago