http://www.nps.gov/yose/planyourvisit/wildpermits.htm
there are no reservable permits available for Happy Isles trailhead for that day, but you might get a walk in if you show up early in the morning on Sep 12. That will allow you to stay in the backpacker campground the night of the 12th and start walking on the 13th.
The same would apply if you started from Sunrise or Cathedral - Tioga trailheads are also extremely popular. There is also a backpacker campground in Tuolumne Meadows campground. Those are $5/night and for the night before or the night after the itinerary on your permit.
The only difficulty you face is that if the fire closing the road isn't over, the road from the valley to Tioga does not open before then, you will not get a permit at all if you plan to exit on Tioga because you can't drive back and the busses are not running. In that instance you will end up hiking in and then back out the same trailhead.
Pay close attention to the rules for backcountry camping at
http://www.nps.gov/yose/planyourvisit/lyv.htm - you will need to be 4 miles from the trailhead on most trails and between Little Yosemite Valley and Happy Isles or Ilillouette drainage and Little Yosemite, you cannot camp at all.
Don't forget to repackage food carefully so it will all fit in the bear canister.
Do take a water purification method. Filter, chemicals (drops or tablets) or enough fuel to boil water, take your pick.
The only other thing... if you're 16, do you have a parent or guardian going with you? because I'm not sure they will issue permits to minors. And you need to have a good map and know how to read it, and some basics of how to navigate...