This has been covered in a frw threads before, but here are
some of the ones I know of ...
Scenic Rim
Darlington Park - Beaudesert (can get busy on holidays)
Flanaagans Reserve - Rathdowney (can get dusty)
Bigriggen - Rathdowney (nice grass sites, altthough no dogs allowed)
Scenic Rim Adventure park - Beaudesert (lots of 4wd tracks - very rough entry road)
Southern Downs
The springs 4x4 park - Just south of Warwick (nice large camping area, clean amenities)
Goomburra NP - Goomburra (limited campsites, popular with grey nomads)
Gordon country - Goomburra (camping and cabins)
Toowoomba
Murphys Creek escape - Murphys creek (nice shady campsites, owners have worked hard since floods to reopen)
Bunya Mountains NP - Bunya mountains (Grassy sites, can get busy)
Kilcoy
Landcruiser Mountain Park - Jimna (can camp anywhere, great 4wding)
That should give you a few options. Most of these places have websites.
I hope that helps
Cheers Chippy