As long as your daughter is enrolled in a public school, even part-time, she must continue to meet that school's specific requirements. As a result, you will have to structure your day in a manner similar to a school classroom. Your daughter will still be required to complete meaningless busywork rather than pursue and explore those subjects she truly loves.
Perhaps with reading and research, you may discover full-time homeschooling is a good alternative for your daughter. Many gifted children currently homeschool. When I speak with homeschooling parents of gifted children their stories are very similar. In school, their kids were bored and not reaching their full potential. According to these parents, the school's gifted classes and programs involved more work but little stimulation, and their kids were rarely challenged. They also felt that competition rather than joyful learning is too often encouraged.
When these parents decided to homeschool, the change in their children was remarkable. It was particularly pronounced in a child with a specific talent, like art or music. Gifted kids have told me that they never knew learning could be so much fun until they began to homeschool. I suggest you read Gifted Education Comes Home : A Case for Self-Directed Homeschooling by Lisa Rivero. You may wish to speak with other families who homeschool in Missouri and see if any gifted homeschool support groups exist.
We also have many resources available for parents who want to learn more about homeschooling. In our How to Homeschool area, you'll find answers to just about all of your homeschool-related questions. Leaving School and Learning at Home contains helpful information about what to expect if you decide to homeschool.
Good luck!