That's the problem, or part of it - the results you get from testing a 2yo are so heavily dependent on factors that have nothing to do with the child's ability.
So your main reason for thinking about testing now is that it's apparently a prerequisite for having her join this group of exceptional children. The obvious thing to do would seem to be to contact whoever's in charge of this group and ask, specifically, what testing they expect for a 2yo and who. locally to you, has done it for other members of the group. Although, TBH, my feeling would be that if this group really expects people to test their 2yos to join, I'd be running fast in the other direction! Maybe what you've heard is not quite accurate, e.g. maybe they expect test results for school-age children only? Or maybe the group is not an appropriate environment for so young a child, however gifted?
You sound a little freaked out about your DD's abilities, but though it's understandable especially since you have a lot of experience with young children (sometimes it's easier to take your own at face value if you haven't a clue how unusual they are!), I think it's premature to be thinking that she's so gifted that you have to see it as a potential problem. She's obviously bright, but that could still be all, or she could be PG - you don't know yet, and even testing wouldn't reliably tell you (OK, it might narrow down the possibilities, at least if the number came back high!) What I mean is that from what you said in your intro post I think she would not have been out of place in the nursery my DS went to at that age, for example (it had no special entry criteria, but it was run by a local university primarily for its staff and students, so a skewed demographic). Of course maybe I'd think differently if I met her, it's hard to write these descriptions of our DC and get over what we see! Still, it might be best all round if you can find ways to get her (and you) congenial company without needing to slap a label on her, and maybe there are ways to do this? If I were you I certainly wouldn't worry about encouraging her interest in reading and maths, although I wouldn't attempt to sit down and teach her either - I'd just answer her questions and make stuff available. Have fun!
