If you drink enough at the trail head, and at each stream intersection, you shouldn't need to carry more than a pint anywhere until you get to iceberg lake. From there, I'd drink all I could, and take 2 liters. Be sure to drink at the stream coming out of UBSL -- it is a significant side trip to get to the lake itself.
You don't need to filter or treat the water. Many of us don't, but you can do what you like in that department.
Switchback 23 may possibly be dry on your way down, but the inlet to the Trail Camp pond is always running clear.
