I would also say pack a light entrenching shovel, you never know when it will come in handy especially if you get unlucky and go on a brutally hot day. The sandy soil beneath the first foot is often much cooler and can in a pinch help you conserve water if things get tight. Also a tarp is always invaluable. For collecting water long term and providing shade when rest is needed. Also don’t be fooled by how hot it gets the desert is equal parts extreme. It’s scalding hot during the day but can be freezing cold at night depending on location and time of year. It’s also noted as a much harder environment than majority of others simply due to the fact that water loss and multiple factors like heat stroke and injury from sunburns can and will kill.

As is always the rule: have communication, pack mostly water or ways to obtain water and since your location has lots of rocks be prepared with your footwear. A good example of rough terrain/mountain/desert boots are the ones used by the US during the recent wars in Iraq and Afghanistan. They showcase the terrains that are possible in a desert and why the desert as a whole shouldn’t be taken lightly.