I am doing Whitney as well and it's going to be my first time. Although I have done other high altitude treks. I've summitted White Mountain peak almost as high as Mt. Whitney as a day hike, and i've also done Mt. Everest base camp to 18,600 ft. which was interesting.
All I can say is that the altitude is more of a problem that fitness. I am not the fittest guy but I consider myself a bit above average, I can do 10 mile hike at sea level without even blinking. I did Mt. Baldy and did not find it difficult at all. However the White Mtn royally kicked my behind, after 13000 ft I just came to a standstill as I just could not find any energy reserve to move my legs...it was that bad. I would move 10 ft and my heart would race like crazy. Only through sheer perseverance I made the summit. I acclimated the prior night at 8000 ft but I think that was completely inadequate.
I plan to do Mt. Whitney as a 2-day hike, acclimating from prior afternoon at 10000 at the Portal and then again at high camp 12000 overnight before the summit so I hope that should be OK.
I also plan to take Diamox, I have a few tablets left over from my EBC trek
Diamox is a LIFESAVER, my o2 levels went from a dangerous 74% at a small Nepalese village 14000ft to 86% at the summit of Kala Pattar almost 19000 ft. I highly doubt I would've made it to that altitude without Diamox.
