Only an hour and a half north of Perth is Lancelin, where you find these desert-like sand dunes. It really looks like a desert when you are there, and since there aren't many people, that feeling becomes more real.
One of the reasons to go there, apart from enjoying this view, is to practice sand boarding. It's a great experience. For a few bucks you can rent a board for a couple of hours.
Totally recommend this trip from Perth. The best way to do it is to have it as a halfway stop before heading to The Pinnacles, another must go during your stay in Perth.