Cecilia,
I'm sorry your daughter is having a tough time. I can relate to what you are going through.

My DS also started 1st grade this year. Last week he commented: "The teacher asks such silly, easy questions. Why doesn't she ask us more difficult questions? I want to learn something new."

He's also having problems finding friends this year. He has told me several times that he feels "different" and "odd" around the other kids.

In the past he preferred to play with girls (I think because the boys are too rough and not verbal enough for him), but many of the girls he played with last year now only want to play with other girls. He told me several times that he's unhappy at school, because he can't find a friend who he's comfortable with, and he's alone at lunch.
He has not been formally identified as gifted, but has all the signs of a HG+ kid. He is very verbal, imaginative and inquisitive, and his passions include geography, animals, art and architecture. He likes making up stories and comes up with great ideas for inventions. He says he wants to be an inventor when he grows up.
I think his social skills are okay- he is an only child, but had lots of play dates last year, and he is very extroverted. (He was very popular last year and gets along with other children.)

We live in a high socio-economic area (so I would've expected to find more kids like him here), and the kids at his school get lots of extra science, art and music programs. They'll place the kids in different reading groups this year, so I'm not worried about that. (He probably reads at a 3rd grade level.)
Right now I'm worried about him fitting in. I sent a message to his teacher, and she said she'll try to help him.

Good luck to you.