Our children sound eerily alike. DS2.25 has been unusually advanced like your DD (though not so much in the written/artistic department), and in a socially obvious way, for most of his life. Being at a similar age and stage to you on this journey, I can't elucidate what the path looks like going forward for children like ours, but I can offer a few points from our experience.
1. Your brief description of the paediatrician sounds like he's sympathetic, maybe even informed about giftedness. That's wonderful; keep him apprised of your DD's development and needs. We're blessed with a paed who is reasonably knowledgeable about (but more importantly, open and sensitive to) gifted needs. At DS' 18 month well-child visit, she was talking about staging multiple grade skips and the ages where the socio-emotional impact is most favourable. Not what I expected to hear, but it was nice to be able to walk into an appointment, speak candidly and be taken seriously, and get thoughtful feedback from a knowledgeable professional.
2. I think EmeraldCity's comment about embracing the "that mom" identity is spot on. No matter what you say or do, some insecure person is going to try to take it out on your DD. People can be so cruel when their self-concept is threatened, and some other parents I've seen seem to get warped enmeshing their identity with their child's development. It's ultimately about choosing allegiance to your DD over others. We need to care more about how our children see us engaging with them, because their development is what ultimately counts for our families.
3. As to navigating comments gracefully, the best advice I have at this age is to project confidence and respond to every reaction when your DD is around as if it were positive or complimentary. Most people, even when feeling threatened, aren't rude enough to shoot down someone who believes strongly in their child. The perceptive ones might even learn from your lead. ETA: There may be a need to switch gears once our children are in school, but I find this works well for now.
4. On the other end of the spectrum-- the hyperbole/freak show fascination-- I think the key is to ensure that most of the people your DD is surrounded by know to take her development in stride.
I remember flushing with admiration at my friend at a Thanksgving party who took DS' (then not quite 2) initiating a conversation with him about gravity as completely normal. He just sat back and said, "That's interesting. Now, do you think everything is affected the same way by gravity?..." And they proceeded to talk about the effect of gravity on objects with different masses. Meanwhile, I grabbed a glass of wine.
Talk a lot about effort, persistence, and process at home, and gently ask those closest to your family to do the same. In our house, knowing a fact receives about 5% of the attention and praise as does muddling through a difficult task independently or coming up with a creative solution. Again, I think this is a case of stacking the odds in your favour by ensuring your DD hears the messages you want her to hear so that discordant outside voices are diluted.
With your family, I would gently broach the subject of letting your DD just "be". She's not a circus act, and it's disrespectful to her to expect her to perform on cue. Encourage people to play with her rather than spectating-- the sillier, the better, IMO. I understand perfectionism crops up early, and if she's already showing warning signs, I'd do an inventory of her day to understand where messaging could be changed. It's a difficult balance, and this is something I struggle with in managing my own parents' admiration for their grandson.
5. I also vouch for the Miraca Gross and Deb Ruf books.
Hope these thoughts help. Please don't be a stranger around here, and do feel free to PM me if ever you want a sympathetic ear going through the same stage.
