When We're Born

Today as I was driving home from church I started to ponder a discussion I had with one of the middle schoolers a few weeks ago. She was confused about the whole "original sin" concept. She couldn't grasp how a child born into this world was already considered sinful when that child was incapable of making any decisions on his or her own. She really felt that children were born good and were of no sin even though once they were able to make decisions they would ultimately make bad ones, bringing out their sinful nature. But she was convinced that the sinful nature didn't make the infant sinful upon birth.
So I got to thinking about how scripture talks about the wages of sin is death. I've known this and heard this throughout my whole life, but this time it really struck me as to how this affects how we look at infant sin. If death really is the consequence for sin, and if babies are born sinless, then why would any baby die before being able to make a decision? Wouldn't they continue on living until sin happened? Either that, or a baby has things going on inside which are sinful that we may not recognize as such.
I'm not going to get into the "where do babies go when they die" debate. I just think it's interesting to think of original sin in this way. I'm sure this is not a new thought, but it just hit me and made sense to me today. Any other thoughts?