ahh! This is a great trip! I've done it twice (in the summer of course), north to south.
The first time, we camped at Trail Camp, left camp at 7am, summited Whitney, then made it to Sky Blue Lake at 6pm. The next day hiked out to Horseshoe Meadows, via Old Army Pass. The second time, also camped at Trail Camp, left camp at 5am, summited, then made it to Soldier Lake at 6pm. I would say I'm average in backpacking speed (I know many who are faster and many who are slower).
Places to camp: (1) at the bottom of the sand hill there is a beautiful, serene lake. You could camp there - it looked as though others have. I think this is often referred to as "Upper Crabtree Lake". (2) not many places to camp until you reach "Huge Blue Lake" (the large lake north of Sky Blue Lake), and then of course (3) Sky Blue Lake is nice (north end looked better to me). Just south of Sky Blue (4) at the bottom of the drop there are a couple trees and I see people camp there. There is a little waterfall from the Sky Blue drainage. (5) Soldier Lake is pretty nice too, but the water is more filthy and there are many more people there.
Enjoy!