I think that ColinsMum's advice is very good. I wouldn't rely on testing done on a 2 y/o as giving you an accurate read on her abilities in the long range. If this group requires testing on that young of a child, they are risking excluding children who would later turn out to be eligible and who just weren't easily testable at that age. They would also risk the opposite -- admitting hothoused little preschoolers who are advanced due to the whole flashcard stuff and whose intelligence scores would wind up somewhat different when older and not being so externally influenced. I'd really start there -- give them a call and find out what, if anything, they even have for a child of that age.
Since others alluded to your other posts, I searched them out

to get more background. Your dd sounds a lot like my girls were at that age. I had no idea that they were gifted. I am just less astute about those things and had less child development experience. At this point, my girls are 10.5 and 8.5. The 10.5 y/o is moderately-highly gifted (98th-99th percentile on IQ tests or 1 in 50 to 1 in 100 people). So, while she is different, she isn't a freak by any means. There are people like her in every group of a reasonable size. What makes my oldest so different is personality, direction, and drive. My younger dd is in the process of being reassessed due to some issues we've had. She is somewhere in the exceptionally to profoundly gifted range (over 99th percentile) based upon earlier test results, but we'll see how these ones play out. She doesn't appear to be gifted at all at this point, but again her personality play a lot into this.
My point is that you can't know where your dd will be in 5 or 10 years or what her needs will be in terms of social interactions, academics, or other things based upon who she is at two. Honestly, had I known that my girls were gifted at two, I might have, like you, sought out other gifted kids for them to hang out with which would have seriously limited their playmate selection. Dd#1 has a friend whom she has known since they were your dd's age. There is a definite ability difference btwn the two and, like you've experienced, at times it has been akward with the other mom. However, dd values this friendship and I have to deal with any difficulities as the adult in order to allow dd to continue to have a friendship she values.
Perhaps your dd can play with older girls sometimes? If she has any specific interests, getting her involved in things surrounding those interests may also help. Our oldest has some very directed interests and she has greatly enjoyed getting involved in scuba diving classes for kids, etc. that align with her interests b/c it allows her to interact with those who share her passions regardless of whether they share her brain wiring. That is good enough often.