I was thinking about this spoiler regarding Sulu and .. isn't it a bit too soon to reveal something so big? Would it have been better if they let the audience get this surprise in the movie? or maybe they want us to obsess over about who could be the mother? but then I guess the other parent is not a character of the crew anyway (unless they go for the mpreg route, we have only one female character and as much as one might not trust this team, making Uhura a cheater is far fetched) and unless it's another character that is known to the trek franchise, there isn't much 'hype' to create about an original character we know nothing about. My guess is that the other parent is in earth or at the very least not aboard the ship, otherwise Sulu wouldn't need to miss his kid and have a pic of her.
The kid looks at least 2-3 to me and if one wants to find a place in canon when it could be possible for Sulu to have a relationship resulting in a kid without that being a one night stand, we could speculate that this relationship happened in the one year it took them to repair the enterprise (mentioned by Kirk in his speech in the end of stid)