To me it doesn't really sound like she really wants to go to school, it sounds more she hasn't been completely "deschooled" and was indoctrinated by pro-school propaganda.
I have been lurking around here for a while and signed up specifically to reply to this comment since I have a ds that age who has been through that "phase". Those who have said 13 is a tough year, I second that. And generally the added pressure of school will not make it easier. Like she herself said she will then be "forced" to do the work, not do it willingly. You are much more likely to retain what has been learned because you wanted to. Do work with her on finding things she has motivation, but make sure she understands that this will most likely not mean that she will learn the same stuff her peers are leaning. One can study things both above and below "grade level" at the same time. Not every adult of the same age is equally knowledge and nobody would demand them to be. But yet it is expected of children.
There is obviously always the option of enrolling in a few selected classes at the local high school or college. You could suggest she try this first, and you both might just be satisfied with her progress and she'll forget about school altogether. I don't know were you are but in some states teens can dual enroll in college for free.
This might sound strange but if she has a favorite show or such, maybe she could write fanfiction? I know most people consider this rather frivolous. But my son learned quite a bit from it (yes, he's a boy writing fanficion). Any kind of "writing" activity, on the computer or by hand is good.
This might sound obvious but: Books! I truly believe that there is a book for everywhere. No need to read Sheakspear or War and Peace. No need to write a report. My son enjoy a large variety of books. Everything from Stephen King and John Grisham to Goosebumps and even picture books. We go to the library every week and let them check out whatever they want, so that would be an idea. How about a mother/daughter book club? Both read the book and then have a book discussion. Audio books are another option.
Also any type of "educational" show. Check out the discovery channel and discovery health. My son retained most of the things he has learned there and was often encouraged to research further as he has a critical mind, because in this words: "Well *I* don't know if that show is just propaganda".
Try board games that teach things such as strategy, spelling and trivial. Think Trivial Persuit or Scrabble. Ah that made me think of these Government simulation pc games ds got into a few months ago. And definitely check out edheads.org. The activities are fun and informative, though impossible to "fail". Yet both of my kids do them over and over again in the way one would replay a beloved video game.
If somehow possible, do get her together with other unschoolers a little older than her. I understand that this is difficult and not always possible. We do not know any other unschoolers. Or anyone who is as crazy as our unschooling, non vaxing, atheistic, non traditional type of family.
I'm sure that you must have some sort of museum or something in your area. Run the idea of just checking such a place out by her. We very much enjoy living museums.
If anything fails you and her could to sit down and create a list of things for her to do in, say a week. This works very well for some home/unschoolers.
Phew, this ended up way longer than I intended for it to be. I hope some of it helps. Please ignore typos and such ....hides....