Again, I have to agree with the posters who said it truly may not be that she's ADD/ADHD, just bored. We went through this on and off with oldest DS all the way through elementary school. When he had teachers who kept the room lively, with lots of activity, and always something different to be doing or go on to if he finished an activity, he excelled. The couple teachers he had who did the "everyone sit quietly in their seats while I teach to the bottom half of the class in a monotone" didn't work so well.
In second grade, his teacher insisted we get him tested, and also told us he wouldn't make it through third grade. Well, we did get him tested, and found out that very definitely he met the criteria for "H" (hyperactivity - I do realize this is much more common for boys), but he had none of the symptoms of ADD. He was the kind of kid who could be reading a book under the desk, talking to a friend, watching another class on the playground at recess and still be able to tell you every word the teacher said. He wasn't unable to pay attention - more like he didn't need to!
If your daughter is that bright, I really think the same things could be happening. This is the son who in 6th grade, we then put in Algebra (8th/9th grade math). Just giving him one class (in his strength) that truly challenged him made an incredible difference in all of them. He was okay being bored in social studies because he could always be working on his math homework when he finished it. It was okay that he didn't really have any homework other than math because he sure had enough of that.
So I guess I'm recommending to see if there's somewhere they could be challenging her more. I'd also recommend against the Ritalin, even if it's suggested. When they did agree that Matt was hyperactive, but not ADD, I'd asked if Ritalin would help. The doctor was very strongly against it. When I said that the teacher had recommended it (does an elementary school teacher have that authority?

), the doctor said that of course many teachers would like their whole classes to be put on it just to make their lives easier! Anyways - good luck, you're obviously a great mommy since you care this much and are doing all you can - and keep us posted.