Are you looking for paid or free camping peter? Biggenden has a great c/p which charges for one night get one free, pay for 7 get another 7 free I understand. I haven't stayed there but Rockylizard has. Biggenden is inland from Childers, my son lives there, its a lovely little town. Going a bit more inland you can find a few freecamps around the dams in that area.
Kumbia which is half way between Kingaroy and Dalby has a great little leafy Apex park, Powered sites that you pay a donation for, also toilets and showers and a BBQ area. I stayed there twice in my novice trip at easter and felt very safe.
Are you looking for Bush Camps (free camps) or Caravan Parks .. as was asked before.
Are you interested in beach areas or bush or small towns.
When do you want to go. A lot of the coastal parks are usually bulging with southerners at present .. but there will still be sites around. Just have to try a bit harder.
Looking just at coastal places ...............
Three hrs or so from Oakey might get you to ....
Hervey Bay ... Lots of choices there (popular but upwards of 13 parks there I think )
Woodgate near Bundaberg is on the beach, quiet & certainly leafy.
Tin Can Bay or Rainbow Beach are worth a look
Noosa River CP is hard to beat but might be lucky to get in there. Just up the road is one at Tewantan. Popular but not what we like .. it's on the river too.
Second best of the Sunshine Coast for us is the Mooloolaba surf front sites under Alex headland. But again you're lucky to get onto the quiet sites there these days but there are some OK ones round the corner near the surf club.
Cotton Tree is large & on the water. Might be busy at present like most coastal ones at present (I suppose)
Dickey Beach at Caloundra is good.
Bongaree on Bribie is small but again good .. lots of winter fishing in the passage.
The Kumbia park is very busy but managed to find a good space both times. The first time I was there for 2 nights, different neighbours each night. On the way home I stayed 4 nights although the limit is supposed to be 2 nights, but I was having a bit of a melt down. Others with mechanical problems stayed over the limit as well with no instructions to move on. Other campers came and went at their will so was always meeting new people. I think if you left it too late in the day you might find it hard to squeeze in and the power boxes would be all taken. Also if you are into watermelon there's a guy on the opposite corner sselling them, has an honesty box. Theres a pub up the road a bit, walking distance and a nice cafe.