Much depends on your particular toddler. Two hours of dancing (plus an intermission) is a lot for any youngster to sit through. If you can bring yourself to do it, you might have a fallback plan of leaving after Act I. The ending (with Clara and the Prince being waved offstage by the assembled Snowflakes and Snow Winds, as well as the Snow Queen, King, and Prince) works well as an evening-ender, and the child would be none the wiser. You, however, might regret the "waste" of money if you have to leave early.
(I'll be in DC, though, and if you'd like to pass off your ticket to me at intermission, I'd take your seat ...

I'd offer to take the kid and let you stay, but even though we're all apparently friendly here at BA, that seems just a little TOO funky.)
As for the production itself, I couldn't be fonder of it. I think it's a great one to bring kids to. The first act party scene is very lush, the battle scene is crowded and hard to follow but exciting nonetheless, and the snow scene is quite magical. If your youngster does not like flashes or loud noises you might prepare them for the cannon shot during the battle, and the flash during the Nutcracker's transformation to the Prince (which is done very well and truly seems like magic).
Act II can drag in places -- I dislike the Arabian variation, which goes on too long, and even thought Waltz of the Flowers is gorgeous it has the potential to drag too -- but the other variations are exciting and short. Chinese, Spanish, and of course Russian are all quick crowd-pleasers. I happen to like the Prince's mime at the opening of the act, and it would probably be worth tipping off the kid ahead of time as to what he's doing. It could get lost as "just more dancing", but if the child knows ahead of time it's a recap they can watch for familiar bits. The corps serves as a sort of chorus during the mime, and their rendition of the mice -- fingers twitching in front of their mouths -- is hilarious. I happen to think that the Prince's lingering glance on Clara as he points to her, then his own shoe before miming its removal and use to conk the Mouse King is one of the glorious moments of the ballet -- seconded by the Prince's retelling of his own fall and triumphant rebirth. But, that's just me.
Something that would help a child of any age enjoy the production is to tell them what to expect, in terms of plot (if you can call it that) and characters. Let them know that some parts will drag, and it's okay to lie across your lap then (quietly), and promise to wake them for the exciting bits. Speaking of which, I forgot Mother Ginger, who is a huge puppet (made by Kermit Love of Muppets fame)! Her Polichinelles, who are the oldest child dancers, are also fun to watch. I also can't say enough about playing the music ahead of time. Recognition is a great tool for keeping a kid's interest. That might be a key to keeping them engaged through Act II.
Let us know what you decide, and let us know how it turns out if you go!