Weather wise, the best time to visit Lawn Hill is about May to early August. These are the "cooler" months and thus better for doing things in. Usually it is pretty dry then, too, though years like this one are a bit of an exception. Up to Easter and a bit after, it can be pretty hot and humid, and wet. From about September it starts to really heat up and the area is quite dry and dusty.
My preference is to be up there late April to end June - when it can still be a bit green.
A really good time to visit that area and stay at Adels Grove is the couple of weeks in June (usually later June) when the palaentologists are there, doing their annual dig at Riversleigh. It is interesting to be around then and various experts often give talks on the subject matter at night. They make it all really interesting. But you would certainly need to book quite a bit ahead at this time. For the months that I have mentioned above, which are the busier months, you need to book ahead, even if it is only a couple of weeks ahead, if you want a decent site. If you want to stay at the National Park, you need to book ahead online anyway.
You have a few options for travel routes from Brisbane. What points of interest you cover along the way will depend on the route - and also on the time available. It is quite possible to take two or three months to go from Brisbane to Lawn Hill and back, via different routes.
For example, you could go north up the coast then strike inland from any of Cairns, Townsville or Rockhampton. Each of these routes is interesting. Or you can go straight inland from Brisbane and there are a few different possible routes that way, too.
Also - do you want to stick to sealed roads all the way?
If you can look at some maps and narrow things down a little, then points of interest can be discussed.
Hi sealed roads where possible but doesn't really matter free camps or parks im set up to bush camp.
Charleville Longreach Winton Lawn Hill Quilpie Windorah Barcaldine Roma and Emerald are places im thinking may have stuff to check out.Maybe do some on the way up and some on the way back.So just trying to see what times I need to spend in each spot to see whats there.
Charleville - couple of nights, including one to take in the Cosmos centre at night. Some interesting historic buildings etc.
Longreach - we took two days to browse the Stockman's Hall of Fame because after a while you need to go away and digest what has been seen before you do the rest. A day to look around in general and take in the Qantas display.
Winton - a day at the dinosaur centre just out of town. An interesting day trip (or place to go bush camp) is Opalton, 120kms to the south: historic opal mining area where you can fossick in mullock heaps. Day to go out to Lark Quarry and the sights out that way. Not sure if the Matilda Centre has reopened after fire, but that is worth some time too. Say 4 nights at least.
Lawn Hill - could fill a week with walking, canoe the Gorges, do Riversleigh tour, do the Adels Grove tour into the back country if it is going, canoe/swim Lawn Hill Ck at Adels, just relax. Ccamping for a couple of nights on the banks of the Gregory River at Gregory Downs is really pleasant too.
Quilpie - maybe only overnight unless you want to go opal mining.
Windorah - pleasant to relax by Cooper Ck but not much to see.
Barcaldine - can see what there is in a day.
Roma - really just a service town. Some big sale yards if you like those!
Emerald - another service town. But it is worth spending a couple of days on the nearby sapphire fields - Rubyvale, Sapphire, The Willows. Also pleasant to relax at caravan park out at Lake Maraboon.
If you are looking to go south from Emerald, there is Carnarvon Gorge National Park which is well worth two or three nights, to walk there.
Of course you need to factor in just relaxing in a camp and enjoying the country that surrounds you.
The first time we went up that way, it took us a couple of months to go from Brisbane to Lawn Hill..........but we don't race around and cram things in all at once.