What Happens to Unbaptized Infants Who Die?

If the doctrine of original sin is true, and everyone is a born sinner on the wrong side of God, what happens to babies who die? Do babies go to hell? Do they go to heaven?

Do they go someplace in between?

Augustine of Hippo said babies go to hell for eternal punishment, but added that they get a mild sort of punishment. If there’s such a thing. The following comes from the Catholic Encyclopedia:

St. Augustine and the African Fathers believed that unbaptized infants share in t...