+1 on Lawn Hill about 80km west of Gregory. Road will be gravel out, but Gregory to Burketown should be sealed all the way now.
There's also camping at the river right at the Gregory town, but it frickin busy during nomad season.
Seeming as you're likely going thru Doomadgee, the Gregory River does flow all the way to the coast and there is a spot off the Greg-Burke Rd when heading to Doomagee (10km off road) that crosses the river. Might be more efficient to stop there overnight.