Sounds as if someone has just finished watching the final episode of M*A*S*H*.
Anyway, I have to agree with some others in that I would find a way to silence the child while not killing it in the stated situation. Killing the child is (if you pardon the rather morbid pun) overkill.
I have to admit that when I read the title I thought you were going to go with a baby Hitler. Even then, I'm not sure if I would kill him without a thought. My hesitation isn't in support of the man he would become but of the course of history that he would have a hand in creating.
Without Hitler, the Twentieth Century would have taken a dramatically different path. All bets would be off if World War II would have even taken place. Without the wartime economy boost, the Great Depression could have carried on for a far greater period of time. While the New Deal did blunt the Depression in the United States, it was war that brought such a swift end to it.
Also, the events started in World War II carried throughout a great portion of the Twentieth Century. Changing or even removing World War II would greatly impact the whole of the Twentieth Century. For example, it was World War II that made the United States a world superpower. This led into butting heads with the Soviet Union and triggering the Cold War after World War II. The Cold War fueled quite a few conflicts in Eastern Asia and Middle East -- not to mention an arms race and a technology race-- as both sides attempted to gain superiority over the other. This lasted all the way till the Soviet Union fell apart in 1991. While killing Hitler wouldn't mean that these events won't take place, it will alter them. Then, all bets are off on what happens in the new Twentieth Century.
The problem with changing history is that no one can be sure of the outcome or even if there will be a net benefit to humanity for changing even a single event. Would the world be a better place if World War II, the Holocaust, and all the events past that point never happened? It is impossible to tell and that's why I wouldn't change a thing.
Maybe I've just watched Back to the Future one too many times to want to tamper with history. Does that make me a bad person?