Zeraph

A knife, always carry a good knife. Also good, thick proven socks. Sunscreen (even in winter one can still get burnt through clouds). Sun glasses. Perhaps something white to cover your neck if your hat doesnt. Probably some kind of net, something to keep out the scorpions when you sleep. Map. I've never used a walking stick...others swear by them, your call. I don't know the exact temps willravel, but it can be warm during the day in deserts, and very cold at night. Some kind of general guide book on the desert and for survival. Some kind of rope/strong string in case you need to make a splint or pitch a water catcher.

I don't know if you need actual survival training for the desert, just read up on it, but again your call if you think you need it. That's just my random thoughts that you didn't specifically list going from most important to least, how much of it you want to bring depends on how cautious you want to be. If it's only a day and a half the biggest thing is knowing where you are and where you are going so you do not get lost and could call for help to tell them where you are if you get injured.

Edit, forgot clothing. You should probably wear comfortable jeans that you know won't be a problem with movement. Id go with a white short sleeve shirt with some kind of extra layer..jacket, sweater, windbreaker to put on incase you get cold. Honestly its hard to say with the exercise you will probably be warm during the day but get cold during the night.