It's not really a big deal to hike Whitney alone for the first time. There are so many books and trip reports available that, by the time you actually hike it, it seems like you have done it before. During the prime hiking hours of, say, 3AM to sunset, you are never alone on the trail. In the pre-dawn hours you will see headlamps ahead and behind. During daylight the trail can actually seem crowded in places. Both camping areas, Outpost and Trail Camps, will have plenty of people. Take a map, tick off the landmarks, and enjoy.