First: be sure you're in shape physically to do this. There is a LOT of elevation gain and loss, Mount Whitney notwithstanding.
Second: Order a copy of "John Muir Trail" 4th edition, 2007, by Elizabeth Wenk and Kathy Morey, http://wildernesspress.com/book328.htm . It lays out the route from N to S and again from S to N. The included maps are not sufficient for land navigation.
Third: I'd suggest starting at Tuolumne Meadows and going west DOWN to Yosemite Valley. That way, your first day starts with 7.7 miles and all of the trail's 1320 feet of elevation gain, followed by 16.5 miles and 5,905 feet of downhill; which gets steeper as you approach Yosemite Valley. This will serve as a great shake-down hike and help get your body and gear ready for Donahue Pass and beyond. Get to TM by 3pm, pick up your permit, and stay at the backpackers' campground that night. It also gives anyone who can't take it the opportunity to bail either in the Valley or back at TM. There are two gear stores and a huge grocery store in Yosemite Village, one of which is a mountaineering shop. Ask the [free] shuttle bus driver where to get off if you need something.
When you call for your permit, explain what you want to do to the ranger. You may need a 2nd and separate Yosemite NP permit allowing you to go from TM down to YV. Do not get a PassThru permit; that will prevent you from camping in Little Yosemite Valley.
My son and I did this in August of this year, taking 2.5 liesurely days to cover the 24.2 miles. We camped at the head of Long Meadow (about 11 miles out), just past the Sunrise High Sierra Camp and again at the backpackers' campground in Little Yosemite Valley. While we could have easily made it all the way down on the 2nd day, we could not have gotten there in time to catch that all-important 5:00 pm YARTS bus back to Tuolumne Meadows, and Yosemite Valley is no place to be without a campground reservation during the tourist season. Besides, the scenery from LYV down is awesome and you'll want to take lots of pictures. Did I mention that it gets REALLY steep (16.5% downgrade) near the valley floor?
Take half a day to rest, eat, and explore Yosemite Valley (wall to wall people and very hot) before taking the bus back to TM. Spend the night in the TM backpackers' campground, and head up Lyell Canyon early the next morning, heading south towards Whitney.
You can leave supplies in one of the many bear boxes in the parking lot of the TM Wilderness Center - where you pick up your permit - so you won't have much in the way of food weight heading down to the valley. YARTS will get you back to TM in time to catch the last park shuttle to the Wilderness Center, where one of you can pick up your resupply from the bear box while the other grabs a site in the campground. Yes, the rangers do check permits and bear canisters there and elsewhere throughout the park.
Of course, if you don't mind a 16.5 mile 6000 foot uphill climb right out of the box, feel free to start from Yosemite Valley.
1) Red's Meadow ($25 package fee)http://www.redsmeadow.com/pdf/PackagePickUp.pdf - or go into Mammoth Lakes which is far better but far more expensive. The shuttle bus fee is $14. It is possible to resupply from the store at RM but selection is limited. Mountain House Freeze-dried meals were available there this summer.
2) Muir Trail Ranch (1.5 days south of Vermillion Valley) so you don't have to climb those 57 switchbacks up Bear Ridge with a freshly-filled 8 or 9 day pack. MTR charges $45 to pack your resupply bucket in by pack train. See their website for details. http://www.muirtrailranch.com/resupply.html
3) Independence or Onion Valley CG. If you are truly lucky and blessed by a friend or relative with nothing else to do, maybe they'll hike from Onion Valley CG up and over Kearsarge Pass to bring you a resupply at the PCT/JMT junction with the Kearsarge Pass trail; that'll save you a 9 mile each way down and back trip. They can even take your trash out with them. Be sure to say "thank you" and pay their expenses.