I think your goal is very attainable. IF you've done some hiking at altitude. It's a long stretch for one day, but very doable.
This summer, I also took a Scout Troop up that way. First day, we went from Horseshoe Meadows, up the Cottonwood Pass, and down to the heart-shaped lake just past Soldier Lake (I think that's the name). We were in a beautiful valley meadow---no other campers near. Altitude hit almost everyone in the group, but we were fine the next morning. There are bear boxes at the opposite end of the lake (Southwestern side).
That camping spot was at about 10,000 feet.
Next couple of days we went up Whitney and out through Trail Crest. We had 3 Scouts, ages 12 and 13, and two adults on the trip, and they all did great. Beautiful way to see the back country, away from many of the crowds on the MMWT.