My suggestion is to determine which is more important: summit at sunrise? or Whitney in a day?. Both are excellent goals but not sure if they can be done together legally (unless you hike real fast) considering the start time you'll need. You probably won't get caught but why "taint" your first Whitney trip with that? Just IMHO.
The two cents worth I'll throw in is to get to trail camp and stay overnight (need an overnight permit obviously) therefore ensuring a early start for a summit sunrise. Not hiking at night will also enable you to see the beauty of the trail as you hike up. The amazing scenery of the Sierras never fails to amaze me and the MMWT is a real gem in that regards. Give yourself extra time to acclimate which sounds like an unknown factor for you at this point. Take it easy for this first trip and enjoy all that is Whitney and consider a day trip next time - you'll know the trail and how you react to altitude. The mountain will always be there.
The Vivian Creek trail on San Gorgonio is a good training hike for Whitney IMO. It's got alot of gain (5600') in a shorter distance (8 miles). I did this hike for the first time as a day hike two weeks after I summitted Whitney and was suprised at how tough it was, especially the first part. The summit of SG is 11,500 so it probably won't help you acclimate but the trail should be a good test of your physical shape.
