J.M.
There are many other ways to have your daughter involved with other children outside of school. Sign her up for some class be it sports, art or other interest area. My daughter makes friends easy also but is shy when an adult starts to ask questions. She is also sensitive and smart and I would suggest you look at your doctor's suggestion. Your daughter is advanced and will lose interest in what the teachers has to say. I am going through this right now and the doctor stated that the teacher should be encouraging her and provide resources because my daughter is bored in class and has started to challenge and question the teacher - which is not a good thing, especially for an "old school" teacher. Last years teacher recommended that we get my daughter tested. But we did not want to push her either and wanted the socialization with the other kids. After this school year ends, we are not going to wait for her to be evaluated if she continues to be advanced and bored. I am disappointed that the private school I am paying to send her to does not care if she can already read at an advanced level. So now every night I am having to make sure that she reads a book at her level. As the reader that was sent home for the first grading period was read by my daughter in less than an hour.
I wish I would have advocated more for her as I did not want to be one of the "bragging" moms on how smart their kid is... so I tried to down play it and "pretended" that it is normal for her to do what she does. After talking with her doctor, I finally realized that I was not "imaging" or thinking that she was advanced. She is ahead and I am no longer going to take "No" from the school or will consider transferring her.
Be aware though if you put her in these other classes that she is placed properly. As you can run into problems with this as well. Second problem I have is that she is tall and most people think she is older. This was part of my problem as I thought when I signed my daughter up for ice skating that she would be placed with her age group. At some point she kept getting pushed to the next group in the same session and eventually it was to high, so she became frustrated. As I was sitting by another parent and was talking with them did I discover she was placed with the 9-10 year olds as she was 6. So I had to speak with the coach. This has happened in several different classes- soccor and gymnastics. Since I was new to this I did not realize it but after the second time it has occur, I now make it a point to let the instructor know she is ONLY 6 years old.
It is quite frustating in an odd sense and I wish you luck. I hope others respond becuase I would like some guidance on what to do- I feel like i am walking in the dark here.