Hi John
We did a similar trip last year. Because we took The Dog we couldn't camp in the national parks. Instead we stayed at Mt Ive Station (Gawler Ranges) and Merna Mora Station (Flinders). Both were bush camping with no facilities unless you went to the homestead for a shower. Closer to each homestead there were some camping areas that had access to power if you needed it (we didn't). We explored the Flinders Ranges on foot, in car and a scenic flight (do it!) and noticed lots of very popular camping areas in the ranges at Parachilna and Brachina Gorges. We drove through the Rawnsley Park Station caravan park and it was HUGE, but if you don't need power then there is a more informal, semi-bush section that is well spaced out.
Eyre Peninsula is fantastic - we are huge fans having travelled and camp in the area three times now. Coffin Bay (caravan park or national park) are both fabulous. Heaps to see and do regardless of the weather and wind direction. Lots of bays, tracks and scenery to explore. Just out of Coffin Bay you can camp at Farm Beach, Greenly Beach or further up the west coast at Elliston, Sheringa, Venus Bay and further north - all great spots. On the east coast there are some free camping areas noted in the Camps 5 book, but we ended up in Port Lincoln. (The Tumby Bay caravan park seemed old and dilapidated, which is a shame as Tumby Bay itself is beautiful - reminded me of Busselton but with islands offshore). Out of Port Lincoln is the Lincoln National Park - we have camped there before. Our favourite spot was September Beach - just beautiful. Most of the campsites in the park had drop-dunnies that were cleaned daily but there is no water. Lots of well marked camping areas (pine bollards and big bushes separate the well spaced campsites). Each location within the park seemed to have only 6 or less camp sites.
Make sure you go to Cactus Beach if you have time. Great camping spot with world renowned surfing history and reputation. It's cheap, basic, firewood and fireplaces provided, drop dunnies, good fishing.
http://myswag.org/forum/index.php?topic=747.msg257192#msg257192A good overnight caravan park on the eastern end of the Nullarbor is at Penong (about 70km west of Ceduna, from memory). They have lots of really big sheds, lean to's and hedges where you can set up your camper and protected from any bad weather.
We accessed all of the above and below places with our Pajero and trailer (first trip) and our Landcruiser & O/B Swan on the other trips.
Coffin Bay National Park (fishing) :
http://teamstozz.aussieblogs.com.au/2011/09/29/coffin-bay-national-park/Mt Ive :
http://myswag.org/forum/index.php?topic=747.msg257184#msg257184Merna Mora :
http://myswag.org/forum/index.php?topic=747.msg257187#msg257187Some more details on the blog too.
Pics from Lincoln National Park