Why do you need to post publicly rather than marking it as unlisted and sharing the link with people you know and trust? Would you personally like to have a video posted of you in your underwear? Even if that's okay with you, perhaps your daughter will grow up preferring to have a more private life, and to keep things like that off the internet? But you've taken that choice away from her.
One of my favorite articles on this topic: https://slate.com/technology/2013/09/facebook-privacy-and-ki... (and a follow-up, after the author was informed that she had unwittingly allowed some photos of her daughter out onto the internet: https://slate.com/technology/2013/09/privacy-facebook-kids-d...). I don't know that I'd go as far as she has, creating a sort of "digital account trust", but I do like the approach of keeping a kid's private life off the internet until they're old enough to decide how much they want to share.