I've always said that you can send your kids to public school with a homeschooler's attitude. What is a homeschooler's attitude? Simple: you, the parent, have primary responsibility for your child's education. The teachers do what they can, and you are appropriately appreciative of and supportive of their work. But you don't expect the teacher to be the alpha and omega of your child's education.
Obviously you need to intervene if the teacher is doing something that is actively interfering with and/or undermining your child's education. But if your child simply wants more, provide that yourself. It's okay if school is primarily an exercise in developing patience and social skills, with most of the academic work happening at home.
In future years/months, if your child gets so far ahead academically that she starts to get seriously bored/disruptive, talk to the teacher/principal about your child doing some volunteer work within the school. Perhaps there's some sorting work in the office she could help with. Maybe she could start a project like a school newspaper, and go do investigative reporting while the other kids are working on something she's already mastered. Perhaps she could help do some intensive one-on-one work with children who are struggling academically.
If you decide to pursue the peer tutor option, remember that teaching others with respect and patience is a powerful skill that takes a while to master. It's very easy for talented kids to think they are helping by giving the struggling child the right answers. This is not helpful! Make sure you give her some specific instruction in how to be a good teacher.
For the academic supplementation you are doing now, her teacher may indeed have some ideas for advanced work she could do. Or you could look up what she'll be studying in first grade and start moving on to that. Or you can do some work in an area that will not be covered by school, like botany.
Whatever you do, please be kind to the teacher and nonjudgmental of the other parents. The same work that is so easy for your child is causing hours of tears and serious family stress for some of the other kids. Kids are different. You happened to get a child who is unusually talented in areas of traditional academics. I've got one too. I've also got one who struggles terribly with traditional academics, though he has many other strengths. Two kids, four years apart, same parents, and the four year old is the better reader. This is life.
Good luck and have fun. Sounds like you have done a great job so far in providing her the resources so that she can excel in her areas of strength. It also sounds like you're making sure she keeps a balanced life. Keep it up.