A couple of questions:
1. How old is your son?
2. Are you planning a day hike or overnight?
My son was 12 when we backpacked the main trail in '01. We got up about 4:30 a.m. at Trail Camp and were on the trail by first light at about 5:30 (first week of July). We made it to the summit by 10:30 or so. Check out the Mt. Whitney trip report under the "highpointing" pulldown of my
WWW site for details.
Depending on the weather, there is a fair chance of afternoon t-storms, so you want to be up and off the summit by noon at the latest. My rule of thumb is 30 minutes per mile plus 30 minutes per thousand feet of gain. Slow that pace down a bit for being above 12,000' as you will be from Trail Camp the rest of the way up.
Be ready for some spectacular views, and enjoy the hike!