Hi Frank,
If you can decide now on the exact dates that you want to hike, there are permits available! Most people wait, so the permits get taken. The permits you need, "Kearsarge Pass JM31" and "Mt. Whitney (Trail Crest Exit) JM35", can be reserved together, and 6 months in advance. Currently, the 6-month window ends at July 7, and you can check what is available. Here's the
Rec.gov link for Inyo permits.
In "Looking For", select "Overnight Exiting Mt Whitney".
Entry Trail: Kearsarge.
I see that there are plenty of the Kearsarge entry permits -- there are 36 reservable slots per day on that trail. So you won't have trouble getting those. The more tricky ones are the exit permits. Only 15 are reservable, and while mid-week exits are available, the July 1-4 window are already reserved below the 7 you would need. (However, that is the only time they are scarce so far.)
The complicated part is that you can't reserve the Kearsarge permit separately from the exit permit, so you have to wait until the 6-month window makes the exit permits available before reserving the trip. Watch the site and the Kearsarge permit numbers closer to the date you want. Once that exit permit date comes available, reserve the trip. I think the next date becomes available at 7 AM.
Edit: (Note, on Jan 6 @11 PM, Jul 7 is available, so it might be 9 PM. Edit: Jan 7, 10 AM, Jul 7 is last available. Aha! Jul 8 slots became available at 9 PM sharp on Jan 7!) Once they become available, they can be reserved in 4 clicks: "Update Availability" on the exit permits, Click the newly opened date, scroll down and click "Book Permit". (You MUST first have (1) your group size set to the number you want, and (2) the Entry Date already selected --the selected date shows gold.) Practice this several times a couple of nights before your exit date actually opens. You can get all the way down to paying for the permit, then cancel it. I had all 15 exit slots tied up tonight for a while. :-)
