Flower, my younger DS (26 months) is exactly the same way. While he's extremely athletic and can keep up with the older gang on his scooter or bike outside, when we're inside he's all about Starfall, puzzles, and books, books, books. He is trying to read everything, and he counts all day long, too. I'm sure you're not hothousing DD, since there's no way I'm doing it to mine either. (I now HS my DYS6, and between that and running around town constantly, it leaves little one-on-one time for little DS during the school year!) It's just who they are.
If your DD is like my DS, she probably just loves to practice her new skils. It's a very common trait in gifted toddlers. IMO, we should just embrace it and enjoy that time together! I do often gently correct (ie, "that's it....seventeen!) if I think it's part of a skill set that he's working on mastering. I usually pick my battles, though, to try and not frustrate him. (for example, mine is making huge strides right now with sentences, so I am trying to encourage that and usually don't correct him when he leaves out articles, etc.)
FWIW, my older son was exactly the same way, and he is extremely social and "popular" around his age-peer friends even while we homeschool. There's no use in worrying about any of that right now. INO, their personalities will lead them through the social issues, not anything we do to encourage their learning!
I agree that most toddler moms aren't in the same place. I probably irritated more than a few moms when my older one was at this stage, since I just figured all the children were around his level. Now I know not to bring these things up at playgroup, and to just nod and smile when someone else brags that their 2 year olds know a few colors or letters.
