Believe it or not, 6:00 AM is about when traffic really starts to pick up in L.A., and for certain, it will be hot and heavy long before you clear the 'Inland Empire'. I'd try to get to bed early the night before, aim to leave by 5, and then stop for breakfast once you clear Banning. The the rest of the day's drive should be a "snap" leaving you a few hours to see Joshua Tree and still make Williams by nightfall.

AZBuck