lewis you'll need a lot more water. Desert's a dry place even in winter. And you should carry as much as you can, well beyond your 'planned' trip duration, just in case of a breakdown.
Be SURE to put a planned route and timetable in the hands of friends or relations that can be counted on to sound the alarm if you are overdue. Consider contacting the local ranger or sheriff's station as well.
And consider this board, there's sections devoted to clubs, regional excursions, future excursions. There are a LOT of off-road clubs that venture out there. A bit of research or advertising should be able to meld your trip with that of a similar group or family. DO NOT GO IN A SOLO VEHICLE. Honey Desert Don't Care. It will kill your family if given half a chance.
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I came of age in L.A., did a lot of offroading and motocross and ATC riding in the high deserts. Mojave. El Mirage. Little Rock. Barstow-to-Vegas. Spent most of my Marine enlistment in CA's wastelands / 29 Palms. This particular incident happened while I was in and it was thoroughly stamped on everybody's brains (afterward) to take proper care and respect for operations in the desert.
http://www.nytimes.com/1989/01/11/u...raining-becomes-a-harsh-lesson-for-corps.html
The corpsemens' slogan after that was 'if you don't have to pee you aren't drinking enough'. It became common practice to order everybody to drink a quart canteen at the top of the hour (but we were working hard in ~115F conditions, garments stiff with salt). Dehydration and its effects on cognition are insidious and you can get in a good bit of trouble with it before you even realize your thirst.
Now that's all a good bit different from a leisurely family outing but the threat environment is much the same. Don't be lulled by your trappings of 'normalcy', 'just another family camping trip'. Bring as much water as you can carry, and then find a way to bring more.