From
http://www.nprsr.qld.gov.au/parks/mo...arney_national
"All camping areas in Mount Barney National Park can only be reached by foot. Minimal impact camping is encouraged within the park; please if you pack it in, pack it out. There are no facilities at the camp sites."
I think that's a 'no'.
In general, the main issue in national parks is that the camping areas may be heavily treed. Not always but often. (In the great outdoors, Europeans tend to seek sun whereas Australians seek shade.) If I were you I'd go as far west as possible to maximise the chances of clear skies - and the trees get shorter and more scattered.
Stopping in a roadside rest area signposted 'No Camping' doesn't automatically meant the coppers will book you, but then again they might. I've heard of people being let camp in 'No Camping' areas because they were 'respectable' and 'not smoking bongs'. Of course, the further out of a town you are the less the chance you will even see a copper. I bigger issue could be the lights from passing traffic. There are some guides to free camping.
http://www.campsaustraliawide.com/
http://www.wikicamps.com.au/
I have the camps book. If you nominate some target areas I'll have a look for spots when I get a chance (and if remember where I put it).