Ok, people seem not to understand that this question doesn't really have a right or wrong answer. They look at this from a purely logical point of view (which is fine) and then say, well now you have to use logic to back up your statement. Fair enough, I will use proof.
There are several ethical theories on the way decisions should be made. Each theory explores a different method of analysing and approaching a moral dilemma. Using a variety of ethical procedures, I will justify my stance.
Natural Law
It is natural that people die of disease. In a world where the population growth is exponential and there are fears of demand on public resources soon exceeding supply, the repercussions of preventing the natural deaths of millions of people must be analysed. Yes, you may be saving the lives of many suffering from the disease but at what cost to their and other's quality of life?
Hedonism
Killing the child will only bring me emotional pain. The fact that I "saved" others is irrelevant as I would be directly responsible for this child's death. Not killing the child is the best way for me to avoid pain.
Ethical Egoism
Killing the child places me in a compromising position. I would have to deal with not only the family of the child (should they come to know) but the public. It would be wiser and much safer for me, both physically and emotionally, to let the child be. I am not directly involved in the deaths of those who suffer from the disease. Therefore, (in the eyes of the general populous) I have no societal obligation to help those suffering with the disease. My safest and best option is therefore to not kill the child and let the others be.
Relativism
In the society we live in, there is a strict taboo against murder; especially the murder of an infant. The overall consensus on morality of the society I live in dictates that I should not kill the child. Therefore, I shouldn't kill the child.