Desert monkeys mean little monkeys in the desert, which means these little monkeys live in the desert. These little monkeys may appear in desert forests or oases. If we simply say that there should be no monkeys in the desert, it is impossible to maintain the survival of these monkeys, because nothing grows in the desert.
Desert mainly refers to the barren land where the ground is completely covered with sand, plants are very scarce, rain is scarce and the air is dry. Desert is also a "sand curtain", an area with drought and water shortage and scarce plants.