Toddler emotions and intelligence level?

My daughter is 2 1/2 and she has been evaluated as a gifted child. They think that she may be at a kindergarten/first grade level with her academic skills, at this point (she will be further tested in preschool). The flip side to this is that when I take her to playgroups, dates, and playgrounds (which I do almost everyday) with, a bunch of kids, she is reluctant to mingle and play. She is more reclusive. If there is only one maybe two children that she knows at the event, then she will, in time, go and play. Sometimes she will sit on my lap during the time and not get involved....even hiding her face. I know that toddlers go through this at times but, this has been a consistant behavior for her. What is the best way that I can help her be more confident in her playtime?