On August 1, 2004, the moon is one day past full. It rises at 9:11 PM and sets at 8:04 AM the next morning. A nice program for sun and moon rise/set times is available at:
http://www.iserv.net/~bsidell/moonrise.htm
You will have a full moon in the sky all night. If the moon is high enough in the sky, you won't need a headlamp except for parts of the trail that are under tree cover. Sometimes, however, the moon is behind the south ridge line and you don't get much light. The exact height of the moon varies over time.