I guess it really comes down to personal feelings on relative values.
Expand the hypothetical situation a little..... If it were between a random adult and a random child, I would usually save the child. But if it were a child and my father or a child and my friend, I would let the child die to save the person close to me. If it were a random r*t*rd*d child and a random adult, I would save the adult because I think that the adult's capacity to live a full and meaningful life offsets the fact that what remains may be shorter. If it were the smartest man in the world who just yesterday found the cure for cancer and was about to publish it and 10 infants, I would save the miracle man because of the many more lives he would save; but if it were the cure finder and my brother, I would save my brother.
I don't buy into the whole "sanctity of human life" deal; I believe that some lives are worth more than others. In general a human life is worth more than a dog, but just like the examples above, that also gets weighed against the value of that life to me personally. My dog is more important to me than the life of a random stranger. In short, relative value is part of the picture but so is self interest.
Expanding on what I said earlier, I would like to say that I mean it in absolute seriousness. It's not something where if in that situation I would change my mind and it's certainly not a joke or fishing trip. Those of you that have seen me post for a while can probably tell the difference. If I take the time to put together a semi-lengthy statement, I'm probably being serious. If I post a quick 1-liner about putting pill boxes on the Rio Grande for instance, good chance I'm kidding around. I have to

at some of the responses. Lot of posts saying that a lot of us "dog people" would change our minds. I can say the same thing; that some of the dog owners that say they would let their pet die couldn't do it when push comes to shove. Short of doing an actual study on this sort of thing which is morally and legally impossible, taking people at their word and assuming that the errors will wash each other out is the best we can do. I also find it amusing how many people are making the moral judgement that the opposite course of action from what they would do is absolutely wrong. As I said before, there's a question of your personal belief on the sanctity of human life and there's a
relative issue. If you believe that all human lives are equally sacred, then I can come up with hypotheticals that test your principles just as easily. For example, someone has a gun to your brother's (or father's, friend's, etc) head and his partner has two guns to two strangers heads. He will either kill your family member or the two strangers and it's your choice. If you believe that all lives are equally sacred then choosing your family member is in effect damning an additional life. But your loved one has much more value to you then a complete stranger. Perhaps you choose him? What about if it's 5 strangers, or 10, or 100, or 1000, or an entire country. Perhaps you choose to save your loved one, but only up to a certain point. The relative value from your perspective is a factor whether you want to admit it or not.