Getting desalinated water into the red centre on that scale would be vastly expensive, on account of the sheer scale of the country. When you are in Alice Springs, the coast is over 1000 miles away in any direction.
It would make the market price of crops far too high. The territory makes big money from mining and tourism, and has the second largest per-capita gross product of all Australian states, although its low population means that total gross product is the eighth largest.
It's hot in the centre - Alice Springs averages around 35 to 36C in the wet season and humidity rises to 70% - it can be almost unbearable, and on one short visit years ago I sat in my car for over an hour in the middle of the night with the engine running and the air-con going full blast. There is never going to be an over population problem there.