In the THEORY of Limbo.
If you reject the THEORY of Limbo, you still have to answer the question: Are unbaptized babies (and other innocents, like the severely retarded) damned?
For later read
YOU have to ANSWER "Where is LIMBO to be found in Catholic writings?"
Let's be clear on what the Bible says first about all people....all have sinned and fall short of the glory of God. We are all born as sinners based on the Word.
Let's go from there to your question.
We do have the example of David's son who died just after birth. David expressed confidence that he would see the boy again. This can only mean Heaven.
This has been called the age of accountability by many....though it is not explicit in the Bible. It is the belief that you have to be of age to know the difference between right and wrong. A number of people say this age of accountability begins somewhere around 10, maybe 12.
As babies and the severely retarded would fall into that category of not being able to discern right and wrong the belief is they would go to Heaven.
The one passage that seems to identify with this topic more than any other is 2 Samuel 12:21–23. The context of these verses is that King David committed adultery with Bathsheba, with a resulting pregnancy. The prophet Nathan was sent by the Lord to inform David that, because of his sin, the Lord would take the child in death. David responded to this by grieving and praying for the child. But once the child was taken, David’s mourning ended. David’s servants were surprised to hear this. They said to King David, “What is this thing that you have done? While the child was alive, you fasted and wept; but when the child died, you arose and ate food.” David’s response was, “While the child was still alive, I fasted and wept; for I said, ‘Who knows, the LORD may be gracious to me, that the child may live.’ But now he has died; why should I fast? Can I bring him back again? I shall go to him, but he will not return to me.” David’s response indicates that those who cannot believe are safe in the Lord. David said that he could go to the child but could not bring the child back to him. Also, and just as important, David seemed to be comforted by this knowledge. In other words, David seemed to be saying that he would see his baby son (in heaven), though he could not bring him back.
Although it is possible that God applies Christ’s payment for sin to those who cannot believe, the Bible does not specifically say that He does this. Therefore, this is a subject about which we should not be adamant or dogmatic. God’s applying Christ’s death to those who cannot believe would seem consistent with His love and mercy. It is our position that God applies Christ’s payment for sin to babies and those who are mentally handicapped, since they are not mentally capable of understanding their sinful state and their need for the Savior, but again we cannot be dogmatic. Of this we are certain: God is loving, holy, merciful, just, and gracious. Whatever God does is always right and good, and He loves children even more than we do. Read more: http://www.gotquestions.org/age-of-accountability.html#ixzz3T3VA7YR6