Tamlee, welcome!
Sept 26 is a Thursday. Check last year's
unused Whitney permits page for the same week. You should be able to walk into the Visitor Center on that Thursday morning, and just pick up some free walk-in overnight permits. There are so many no-shows and cancellations that go unused, you should have no trouble.
If you want to be more sure, if you check the online recreation.gov site for the permits (
bookmark this link) and keep checking, especially the week before the hike, you may be able to snag permits that other people have decided to release. (But you pay $15 each for those.)
Also, the unused permits become available starting Wednesday morning starting at 8 AM, as others picking up their reserved permits drop off a slot or two. The final time that they declare the no-shows available would be Thursday at 11 AM for hikers starting on Thursday.
Finally, as you can see on the unused permits page, you are sure to get a dayhike permit for Friday.