Welcome greenlotus,
As Amy suggested, I'd start by finding out what programs are available in your school district for intellectually gifted students. I'm also curious - your other dd is apparently subject accelerated in math (?) Is she older? How did her math acceleration happen - was it teacher-suggested, test-led-to-school doing it, or did you request it? If it happened due to some type of school prompt (teacher, testing, whatever), and if your dd is in the same school, I'd suspect you might have input from the school as a follow-up on her Iowa and Gogat scores. *Maybe!* (there are many of us here who haven't!).
You might also want to check into private schools and/or alternative public schools in your area. It took awhile for us, but we found a good fit through private school which, even though it's not a gifted-specific school, has teachers that understand gifted children, a flexible program that offers advanced academics, and an all-around good program for social development through the elementary school years.
She wasn't running around reading medical texts or doing advance geometry like some kids I read about.
I think it's important to realize that all kids are different, even highly and profoundly gifted children. The idea of an extremely high IQ child running around reading medical texts or doing advanced mathematics at an early age is simply a stereotype- nothing more. Someplace, somewhere (and I'm sure likely here at this forum) there are a few kids doing that. I suspect there are just as many PG kiddos (perhaps many more) who are out playing in the sandbox or with their Barbies when they are young. The thing that always stood out for me, with my EG ds (who, btw, is again, just one example of one gifted kid), was his insight and the complexity of questions that he asked at a very young age, as well as how quickly he absorbed and retained information.
But she was having a terrible time socially, and asked to see a therapist to help her with "her friendship troubles" (DH and I are therapists).
The social issues might be related to a not-great fit at school in terms of intellectual peers - or it could be a not-so-great fit simply in terms of other peers. Early elementary was like a mine-field socially for one of my dds, not because of IQ differences and lack of challenge in school, but because the girls in her grade were testing social stuff all over the place, creating clubs, breaking up clubs, vying for friendships one day, tossing them out like the wind the next. Social stuff at school can be tough in many different ways. Your dd has wonderful insight and she's asked for help with it - I'd try to help in two ways. The first is to look at school fit - what exactly is going on? Is there more than just an academic/intellectual mismatch? The second is, I'd honor her request for finding a way to work on social skills - even if you don't personally think she needs the help. It doesn't have to be actual therapy - maybe you have a friend who's also a therapist who could meet with her informally, take her out for an ice cream date or something, and talk to her about this. Or you could work with her (if she's ok with that). Or you could brainstorm other ways of working on it with her - things like playmates etc.
Hope some of that helps!
polarbear