Dogs can be walked on paved and dirt roads, but not on hiking trails. They're permitted to wander on leash up to 100 yards from the road, and there are plenty of small dirt roads where you'll be far from most traffic. Leashes are the law here, but they're also a very good idea because of critters like mountain lions and bobcats. Dogs sometimes rub up against the prickly plants or try to bit them and end up with a major problem. If you wouldn't want to walk barefoot here, neither would your dog.
Rangers report several cases of paw pad injury each year because of the hot ground.
Come when its cooler and you'll be better off. However, the 100 sites at Black Rock Canyon require reservations. Always bring lots of water on your hikes here, and make sure your dog gets her fill. It doesn't usually get nearly as hot as in other parts of the desert, but you don't want to take a chance. From Interstate 10, exit at Highway 62 and drive northeast for about 39 miles to the town of Twentynine Palms.