I may not have as much experience on Whitney as many on this board, but I have been on top three out of the four attempts that I have made. My first time I got hit hard by altitude sickness at Trail Camp, and going down was a chore - going up was absolutely out of the question. I have always had summit fever, so it was a hard decision to turn back. But, as they say, the mountain was there still there the next month when I went back for my first successful summit.
The next time I tried it in one day, I started at 3:30 AM, and got back down to Portal at about 6:30 PM with an hour on the summit. Be prepared for weather, drink plenty of water (last year, from Guitar Lake to Outpost Camp, I ran out of water after drinking 4L), and don't carry any more weight than you absolutely have to.
Conditioning is very important. There is a huge difference between running on a treadmill at sea level and hiking a trail above 12,000'. You need to get in some time on mountain trails. And sleep high before you start (Portal, Horseshoe Meadow, or White Mountain). Another trick that I have learned is that aspirin will thin your blood and reduce altitude sickness, which has always been a problem for me. Just realize that if you thin your blood, any injuries will bleed more.