There are so many variables to deal with when hiking Whitney -- including altitude, personal fitness, trail conditions, weather, nearby fires, length of visible sunlight, and potentially routefinding if it has snowed, or snows while you are on the mountain. It sounds like you are thinking of doing this hike by yourself, which adds another dimension. At least during peak season, there are lots of people on the trail, and people often help each other when issues small and large arise.
My first time up Whitney was last July (2010). Permitless, I drove the 370 miles from the Bay Area to Whitney with my dog. Got a walk in (overnight) permit for a Friday entry in peak season in July. Had a nice time camping at Outpost Camp. My pup and I went up to Trail Camp, scoped it out, talked to people. Then we hiked back down, got my tent and stuff, and left the portal. An unexpected but lovely 1-night trip learning the mountain before my September 2010 summit trip.
The point is, with a little flexibility, you WILL score a permit while the weather is still good, other people are on the trail, and routefinding and snowskills are not an issue, particularly if you go midweek. That way, you can eliminate some of the variables that could otherwise pose significant challenges (and potential risks) to a first attempt.
