Yes, if that were all oft there wouldn't be much of a problem, but her age factors into other things as well. If she had already been 16, there would not have been any need to postpone her wedding with Joffrey for a few years, also some parts of the story of ACOK regarding her and Tyrion would have to be changed.
But it's probably not that difficult to think of another reason for these things. Maybe Ned wants to give their children a chance to get to know each other first (although it's not as if they had much of a choice...)
