I did this as a backpack. In Rocky Branch up to Stairs where we camped for the night. Be sure to drop down to Resolution Shelter to pick up water before climbing Stairs though. A bit of a PITA, but well worth it. We brought enough water for the entire next day because we were worried that the spring nartreb mentioned would be dry (it was a very dry summer). As it turns out, we probably could have gotten water there, but it was running pretty slowly. My best guess is that with all the rain we've had, it MIGHT be reliable, but DO NOT take my word for it as my info is several years old.
From Stairs we hiked up to Davis and Isolation then down to Rocky Branch shelter (can never remember which # it is). We stayed the night just past the shelter (lots of spots for tents) and headed out the next day.
A fine trip! Enjoy! And I highly recommend staying on top of Stairs. It's one of the most beautiful places I've camped. My friend slept on the ledge (I was sure he would roll off!) and I tented at the designated tent site.