Ok, let me give you a short course in California's compulsory education code:
There is no homeschool statute, but we do have a court case. Yay.
Children in California must be enrolled in a private school or a public school, or tutored full-time by a credentialed teacher (and at the high school level, the tutor must be credentialed in each subject).
Private schools are not regulated by the state, other than having to file an affidavit annually.
The court case of a couple of years ago decided that homeschoolers are the equivalent of private schools.
So yes, you must either file an affidavit yourself, which makes you a private school with one student
or you can enroll in a private school which also enrolls homeschooled students. The court referred to these schools as "Private School Satellite Programs"--PSP. Some PSPs have a campus with children who show up daily; some only enroll homeschooled children. Both campus and non-campus private schools look the same on paper.
If you teach her at home, you decide when she is ready to be graduated, and you issue a diploma. The state is not involved--remember that she would be enrolled in a *private* school, not a government school (such as the charter school), and the state has no jurisdiction over private schools (other than requiring that affidavits be filed annually). So you (and she) decide what she must do to be graduated, and when she completes that, you graduate her, give her a diploma, have a party.
Public school students have to take an exit exam. Private school students do not.
There is a test called the California High School Proficiency Exam (CHSPE), which is the equivalent of a high school diploma in California. Students who are in the second semester of 10th grade, or who are 16yo, make take the CHSPE, and if they pass, they are considered graduated. Some homeschoolers have their dc take the CHSPE, but it is not required; it does sometimes help younger children who want to enroll in community college...but that's a whole other thread, lol.
ETA: Los Angeles has always been hostile to homeschoolers. They have no legal clout at all, but they still try to make things difficult for homeschoolers. If I were you, I'd join HSLDA before trying to withdraw your dc from school, just for peace of mind.