Fast-travel to hidden valley. Immediately turn around to face South-East, and walk in a straight line until you get to a gap in the fence. Follow the canyon forward (lots of scorps) until you pass one body, keep going in SE direction until you come to a big crater/hollow, with lots of scorps in it. The pistol is on a rock at the bottom of that crater.
I had problems with this too, but found the possible fix for it. First you have to talk to the supply person to initiate the unmarked mission/quest. Once that is done you have to talk to the quartermaster at the firing range the guy that sits behind the desk. You absolutely have to talk to him so you can be directed to Initiate Stanton *think that's his name* who will talk about Scorpion Gulch. Found this place and had not talked to the QM to get Stanton to talk and as a result found no missing laser pistol. However after speaking to the QM and Stanton the pistol appeared right on the rock as you zone into Scorpion Gulch from fast traveling.
However I do have to warn that if you do fast travel you will be ambushed by atleast 4 to 7 giant scorpions. The laser pistol is on a rock in the center of the arena like area. Also to note when you loot the item it won't go into your weapons area, but into your Misc. section as Missing Laser Pistol.