I don't know about Australia, but I do know that in the Sahara there are quite a few spectacular mountain ranges; the Ahaggar Mountains come to mind, as well as the Tibesti, the Adrar des Ifoghas and the Aïr. They are not known for their lush rainy climate...
Hoggar National Park, Assekrem, Tamanrasset, Algeria. Photograph by Mohammed Amri, available on Wikimedia under the Creative Commons Attribution-Share Alike 4.0 International license.
Satellite image of Tarso Toon (top right) and the Ehi Yéy (bottom left) extinct volcanoes in the Tibesti mountain range. Image available on Wikimedia, public domain.
Aïr Mountains in the Sahara. Landsat 8 satellite image, May 26, 2013. Photograph available on Wikimedia, public domain.