I am a 19 year old college student. I do know that babies and young children are going to heaven, because our God is a merciful God. I recently got into a tiff with my boyfriend about how they are saved. He says they are saved by faith that He gives the children (Matt 19:13-15) he says not to offend the little ones who believe in me. I think it has to be a personal choice and children are saved because of their innocence.
Babies cannot be saved by faith because they do not have the capacity to believe. One must be able to understand that Jesus is the son of God and that he died on the cross and shed his blood for our salvation in order to believe on Jesus (Matthew 16:16). Also note that faith is not faith unless it is living and active. James says that faith without works is dead (James 2:20). If babies have faith, then it is a dead faith because they do not have the ability to do good deeds. James also says that even the demons believe and tremble (James 2:19). No one can be justified by faith only (James 2:24).
Second, babies don't have to be saved, because they are safe. Sin is what separates man from God (Isaiah 59:2). In order to sin, I have to do lawless deeds (1 John 2:15). If babies cannot do lawless deeds, then they have no sin. If they have no sin, then they are not separated from God. Hence, until they grow up enough to know right from wrong, they can't commit sin and they are safe.
Matthew 19:13-15 teaches nothing less than the innocence of babies and young children, not their guilt and need for faith. Jesus reference to "faith" in children is to their ability to trust, not their ability to reason and believe a particular teaching. Children are naturally trusting which is what makes them such easy prey for evil doers in this world. Jesus exhorts his disciples to have that child-like faith in God because God will never do us harm.