Nei, I've only day hiked Whitney, but if I was doing an overnighter, I'd still leave early like at 6/7 AM. I don't know how strong/healthy you are, but even with a heavy pack, I assume you would be able to get to Trail Camp within 6-7 hours tops.
You'll have plenty of light, and on those dates, see plenty of people. It will be hard for you to get lost. Trail Camp has a lot of wide, dry space to camp. You'll have plenty of people there to chit chat with and probably summit together the following day.
Leaving at that time, the snow will still be relatively firm, and you'll have a healthy cushion to set up camp, take pictures, enjoy yourself, (see if you get AMS, and if so, how bad), etc.