Hagrid picked him up as a baby for the same reason he picked him up to go to Hogwarts. Hagrid is one of the best protectors you could have and is completely trustworthy. Plus, you never hear of anyone apparating with an infant. In fact, I have read so much fanfic that I am not sure if side-apparition is something that is canon or not. Thinking back on it, I don't think it is. So could it be you cannot actually apparate with someone else at all, or is it that it is just too dangerous to apparate with an infant?