Brisbane to Simpson

Well as you need to get a Desert Parks Pass, you could just do 2 lines in the SA part, any of the 3 legs in either direction (French, WAA lines, or Rig Rd).

But if you're reasonably setup for desert travel, you could do any of the routes from Birdsville to Mt Dare, then do Madigan Line back from there which brings you back to Eyre Ck, and the little return on QAA to Big Red.

Bear in mind the desert will be mad with people crossing, but doing it this way you can avoid some of the main crowd on the return leg.

Madigan used to be remote / have an isolated feel to it, now it's more travelled.
You will need to get the free permit for that from the central land council, easy to do online.

You could go to BV via a southern route through Innamincka, then Walkers X or Cordillo, and maybe a route via Windorah back.

I've done both ways ex Brisbane, and they are both interesting.

Have you been out that way / Central Australia anywhere before, and how far do you travel maximum distance wise each day?
There is heaps to see out there, Currawinya National Park between Eulo and Hungerford with it's shearing shed that is probably the best maintained shed i've seen is a park well worth exploring, Sturt National Park near Tibboburra with it's jump ups has stunning scenery, Cameron Corner and Haddon Corners are out there to tick off the have visited list, then Burke and Wills Dig Tree and associated graves and markers, Coongie Lakes etc around Innamincka are there to see, then if you decide to cross the Simpson Desert you can head up Finke way to Lamberts Centre of Australia and come back down the Oodnadatta Track with all it's rail history...there's all that and so much more to see, that you'll need to just pick some and come back again to do others.
I think if you have your heart set on crossing The Simpson you have to head straight to Birdsville which is gojng to be about 3 or 4 days gone already possibly even 5 days depending on how far you want to drive each day, and possibly means lots of kilometres to cover with not much time at all to look around. Thargomindah is about 1000klms from Brisbane for example, i did that in a day back in July but others take atleast 2 or 3 days to cover that distance....then it's onto Innamincka and Birdsville which knocks another few days off, can be done in a very big day though if you don't look at anything (personally I enjoyed Walkers Crossing route more then Cordillo Downs route, but either is a nice enough drive), but it's more like 2 days....so straight away you're down i'll say a minimum of 3 big days of just driving, but more like 4 or 5 days if you want a holiday of sorts.... then say 3 or 4 days to cross the desert and leaves X amount of days to get back to Birdsville (maybe you'll later have to detour to Coober Pedy for supplies as well?). My choice would be hoof it to Lamberts Centre after crossing the desert, then do Oodnadatta and Strezlecki Tracks back to Birdsville, checking out the rail history along the way, but it's a hell of an overall drive to do in 12 days, not for someone not liking to driving big distances on outback roads each day.....it's definitely doable though and a trip some people will love, but for others it'll be far from a relaxing holiday and they'll be exhausted afterwards and needing a holiday to recover.
Another option is to do The Simpson another time, take your time getting to Birdsville via Currawinya and Sturt National Parks, onto Cameron Corner then Innamincka area to look around, tick off Haddon Corner also if that's your thing or just onto Birdsville via Walkers Crossing (if open) or Cordillo Downs routes....just depends what you want to see really and how much driving you want to do each day.