We brought our dog for Thanksgiving a few years back and it was fine. Essentially the same rules as the majority of National Parks. Most of the parks I wouldn't consider "dog friendly", but Death Valley was easier than a place like Yellowstone. Good part is that time of year it's cool enough to leave the dog in the car if you do want to do any of the trails or viewing areas. All those are off limits for dogs. We kept ours on the leash and just walked her on the dirt roads by our campsite. Note do prepare for some extreme weather that time of year, the higher elevations can get a lot of snow. We camped down at sea level which was comfortable maybe dropping to 40 overnight. But out exploring even the racetrack and that level was all snow covered.
www.nps.gov