I don't know if you have anyone driving and helping you, but you could do the first two days without any load: HI (Happy Isles) to TM (Tuolumne Meadows) and TM to RM (Reds Meadows).
The first leg is not bad (I've day hiked it, only the opposite direction). The second is a long day. I think AlanK and his son have done that one in a day. (Hoping Alan will describe his experience.)
I don't think the altitude will be an issue starting on the north end, since both passes are only about 10K.
No permit required to day hike out of Yosemite. But you would then need a permit out of Reds Meadow, and that would be the Inyo N.F. wilderness permit, so the Whitney Trail Crest exit permit would also be required. Best get a permit in Yosemite that will carry you all the way (whether you overnight on the trail or in TM.)
By the way, that's a huge elevation gain the first day out of HI, so staying near TM rather than below Donohue Pass might be in order.
