What you are describing is a child who has quite complex, fascinating and high-level stuff going on in her head - while surrounded by quite simple, not-terribly-interesting, low-level stuff. Is it any wonder she's choosing to spend more time in her head? If she generally has difficulty engaging with people and other environments, then you might have some red flags, but if it is just at school, then I would look first to a mismatch between the school and her needs before assuming anything might be wrong with the child herself.
As for talking with her teachers - well, sigh. That can be tough. It's a rare teacher who is willing and able to accept even the possibility of giftedness and three-year-old in the same sentence. I would tend to avoid the "G" word. Instead, I think you said it nicely: "DD is not really “lagging behind”, but just has unique interests and capabilities not on par with rest of the children in the class." Ever so very gently and politely, help them see what you see: the kinds of books she can't get enough of, the activities, discussions and people she *will* engage with, and how these are different from her classroom. Allow them to draw the conclusion themselves, if possible, that she can and does apply all the skills they don't see, when the content/ activity is a better fit for her.
