Pick of the campspots are (in my opinion)
Along the river with beaches: -32.340865,142.479415
Put this gps co-ord into Google maps. All the dirt roads you'll need to travel will be shown here. All up approx 15min from hwy.
As for the vehicle, it will all depend on how dry the roads are. Any sign of water on them and unless your in a 4wd with mud tires, don't bother.
If it's dry, then there will be no problem, the roads in general are in good cond and used frequently.
We used to travel there in a Toyota Starlet from Broken Hill and as long as you keep the speed under 60km/h, there will be no probs.
However, if you do encounter rain whilst your there, get out asap, will take approx 10-15 min to get out. The roads along the river in particular are grey river clay, hard as a rock when dry, but the minute they get damp, they turn into ice and you'll be digging your vehicle out for days
Most of the major dirt roads you'll be travelling along will be identicle to the pic in my signature (the one on the left hand side)