I could read and write at age four as well (and like your daughter, WANTED to do it). I was going to attend private school and was given a "kindergarten readiness" test because their curriculum was more advanced than public schools.
After taking the test, my parents and the school decided to place me into 1st grade instead of K. (I was a young five when I started 1st grade.) I did very well academically, and my class was so small (8 kids) that the teacher could give me separate reading books and challenge me more easily than a public school teacher might have. (In addition, the kids were all middle class, spoke English, had involved parents, etc., so the challenges for this teacher were much less than what you would find in a traditional school setting.)
My social development was a different story, however. None of the first graders wanted to play with a five year old. (Kids are so age-obsessed in the lower elementary grades.) I did have one friend, and got through the year OK. The next year I moved up to second grade, but they sent me to do reading in the 5th grade room, etc. Again, academically I was fine, but it was very hard for a six year old to make friends with kids in 5th grade.
I don't have any sage advice, just wanted you to make sure you considered every angle before making a decision.
