This is probably not a popular view, but it is one that I hold. I am not rabid about this; I don't go around trying to debate the point with parents who have chosen to do this, but I am pretty opinionated.
I do not think children should be baptized. I don't think there should be a rule about it, but I think it is bad practice.
Think about it: Baptism is a sign, it is a covenant. You are making a commitment to step out of one way of life and into another. The old man is dying, the new man is rising. You are exchanging one life for another.
How does a child do this? How do they weigh this out? What life are they exchanging?
Can I be honest? Isn't this more about the parent than the child? Isn't it more about the parent feeling safe and affirmed? Kodak moment?
Having taught for 18 years, I have found this to be true: Most children parrot the thoughts and opinions of their parents. Their politics and spirituality are all picked up from their parents' wake. Their is very little personal insight in their worldview.
So then I ask: Does it not cheapen baptism to direct a child into it? Are we not announcing that baptism is not really all that important, if a certain amount of soul searching is not needed in the decision process?
I do not think scripture's silence on this is a clincher for my case, but I believe it does lend some weight. You do not see children being baptized in scripture. I believe that is because the apostles understood that a child simply does not have the faculties or experience to make such a decision.
So how old then? Again, I do not desire hard and fast rules on this but I would ask believers to consider: If you do not think your child is old enough to select a spouse, why would you direct them into a decision of baptism? Is not baptism, in many ways, a more important decision than marriage?