I think the biggest question mark is the ability to go from sea level up to 13k in an afternoon. Mt. Dana is short but steep. It can be done in 4-5 hours from what I've heard. Definitely not by me!
If you can get up there, it would be a good thing. Any time spent in the higher elevations prior to your hike will be beneficial to your chances of success. Almost all of my successful Whitney summits all have fallen after a week long trip up at the June Lake Loop, which is near Tioga Pass where you're going. Every time I've tried to go straight to Whitney from home, it's been a turnaround somewhere between Trail Camp and Trail Crest.
