Rockman, that trail starts at 6300' and the pass is 12,000. It is a long way up and over. People use it to climb Mt. Williamson and Tyndall, but otherwise, it is a huge climb. When I did it, we started in the evening, and hiked until midnight, camped, and then climbed all day to gain the pass late the next afternoon.
You might consider your alternatives: Lots of people get reservations and then either cancel in advance, or just don't show up for their permits. Check the unused permits numbers
in this thread, and you can see that on practically any day, you can get a Mt Whitney Main Trail overnight permit just by walking in on the day you want to start your hike. In addition, the Horseshoe meadows trail head has a quota reserved for walk-in requests. And the Trail Crest exit permits also have a walk-in quota.
If you get to the Visitor Center in Lone Pine before 11 am, you can probably put together a more enjoyable hike on the spot.
If you want to be 100% sure of your itinerary before you arrive in Lone Pine, you might try calling the Wilderness Permit number in the week before your hike, because
the nicer hikers who can't go will call in and release their reservations a few days before their hike. If you get a reservation that way, though, it will cost you the $15 per hiker, while walk-in permits are free.