Advice for a newby...

cant speak for the Tanami but unless the GRR has changed in the last 4 years then the Delica would be fine. Fuel range is also adequate as there are a few places to fill up on the GRR However a jerry or 2 is always good backup for if you do some extended poking around or make some miscalculation.
Check the hight of the King Edward river however if going to Mitchel falls as this is the one river crossing on the GRR that may pose problems.
Be aware that depending on the wet late april is about the earliest things will really start to open with some spots remaining closed
I went on early march 03 after a weak wet and bell gorge was closed and Mitchel falls was not long open with around 700mm at the King edward xing

Tanami track will be more than likely corrugated but if you slow down , drive to the conditions and look out for the lunatic Locals in 2 wheel drives all should be well and you will enjoy the trip, Oh and don't forget to visit Wolfe Creek Crater.

Doug

Kath, just bearing in mind what the others are saying, I would also be making sure the tyres I have on the Delica are meaty enough to cope with the tripping. Slightly agressive tread and deep enough. Good condition to do the journey in other words.