pen replied:

Kate,
If you give the following two blokes a ring, they can give you up to date info on the Tanami. Frank, Yuendumu Mining Co., fuel outlet at Yuendumu Community, (08) 8956 4040 & Bruce at Rabbit Flat Roadhouse, (08) 8956 8744. They're great blokes. There's a very good bush campground at Rabbit Flat. Tilmouth Well at the end of the bitumen has a campground & cabins and are very good.
Cheers,
pen

Tony replied:

Kate, My wife and I crossed the Tanami last September on the way back from the Kimberly Area, and had no problems at all. You can now camp at Wolfe Creek Crater, there's no showers but nice clean toilets. Have a good trip Tony