Hey Smidge,
Methinks you have come to the right place. After having been on the receiving end of various comments ranging from disbelief to fear and to criticisms of hot-housing ('cause of course I must have tied my hot-headed 12 month old to his high chair and force-fed flashcards to him 'til he got his alphabet DOWN baby

), I just decided to save my stories of pride, joy and apprehension for this forum and close family members or friends should they ask. With time, I realized that as long as you have a small number of people in the know, that is all you need. For the rest, either you try to live with the fact that you can't share certain things with them and talk about other things or just spend less or no time with them (easier said than done but it is possible, because in the end what is more important, fair-weather friendships or your child's well-being?).
Maybe try to communicate more with your daughter about how she feels and what she wishes. If she wants to go to the playground, maybe tell her that in playgrounds, kids can be rough but it's usually not personal. Give her time to explore her environment with you on the bench until she is ready to go explore. Anything to help alleviate her anxiety to help avoid isolation. And read a lot about how to deal with overexcitabilities in gifted children. It helped us a lot with dealing with our easily frustrated and sensitive (yet terrific) tyke...
Also is there a gifted kids association in your town/county, maybe they can help with suggestions?
And last but not least, know that you are not alone. Welcome!