I would suggest a Arrma Mojave Grom. Brushed ones are 150 (USD) and the 223s brushless ones (faster one) is 200-230 (USD)
There's also the Latraxx (traxxas) prerunner which is 130 (USD) but I would take the Mojave over the traxxas.
Most other desert trucks or trophy trucks are 1/10 or bigger and more than 500 bucks. The mini ones are cheap but a blast to drive.
Or if you are looking for a bigger car, a Short Course Truck (Slash is most popular) would be the closest to a desert truck. Can convert it to a long travel suspension and it would probably be a bit cheaper than the bigger desert trucks. (Mainly from Traxxas, Arrma or Losi) Over here in the US I can usually find 2wd slashes used for around 125-230 bucks depending on what electronics, upgrades and condition. Not sure on the NZ market.