The White Mountain training hike is excellent advice. Drive up the night before, sleep in or by the car at the gate at 12,000' elevation, and hike the 7 miles to the summit and back the next day.
That will give you a good idea how your system reacts to the altitude. And if you do it in the week before Whitney, you will gain some acclimatization for Mt Whitney, in the process.
Make sure of the road conditions to White Mountain before you go. And you need to haul all your water on the White Mountain trip.
