depending on exactly where you are going you will need a South Australian Desert Pass which comes in a pack including maps and safety information. You might also need to purchase a Qld desert camp pass - see links below for further information and to order your passes.
Department of Environment and Natural Resources - Parks Passes
Simpson Desert National Park - About Simpson Desert (Department of Environment and Resource Management)
http://www.environment.sa.gov.au/parks/sanpr/simpsondesertcp/visit.html
we are heading off next month (from Brissy) going south around the simpson and then crossing back across the simpson - hopefully we'll get through, but at this stage it looks like we will get to within 70ks of Birdsville and have to turn around and come back (can't cross the river) - so at least we get to do the simpson twice!
It's very wet around there and a lot of roads are still cut, so you might want to have a plan "B" and lots of fuel - I'm happy to throw you all of our info and you can use or discard as required.
cheers
de