The war in Africa wasn't that long or drawn out, a few months, maybe. Besides, is a desert terrain even needed? No, The Aussie deserts weren't the battleground anyway. Just because Australia was in the war doesn't mean the battles were fought in the middle of the desert. Most action took place in the Pacific.
P.S. watch the
Pacific, it will give you an understanding of why Australia was so important to both sides. Just watch it. You will understand why the war was mostly in the Pacific Isles. (Guadalcanal, Okinawa, Peleliu, etc).All islands in the Pacific ocean, not in the desert.