I love the desert. As others mentioned, water is most important. If you can, choose a car with a full size spare. ( I purchased an extra rim and full size spare since I camp in the desert a lot.)
Fill up whenever possible
Wide Brimmed Straw Hat (much cooler than cotton or synthetic)
Umbrella (Light colors. Not mandatory but makes a nice portable sun shade)
Map
Chapstick
Hand Lotion/Vaseline (the low humidity is hard on your skin)
If you've got sinus issues, a saline nasal spray might help. Did I mention its dry?
Have a fun trip!