ANSWER: First, it needs to made clear that the Bible says that those who are not saved at death do NOT go and spend the rest of eternity in some every-burning Hell. The truth is they are DEAD, unconscious of everything and everyone, until God resurrects them in a future judgment. This is true for babies (even those who are aborted) as well as for adults. It may seem hard to believe that people could receive salvation after they die, but they do!
There is a quite interesting passage in Ezekiel 3 which is commonly referred to as the valley of dry bones. In the Old Testament, the vast majority of ancient Israel was never "saved" as we would define it today. When they are resurrected in the near future, as Ezekiel's vision shows, they will NOT be thrown into a lake of fire to be punished forever. Rather, they are brought back to a physical life where they then will go back and live in the land of Israel.
"Behold, O My people, I will open your graves and cause you to come up from your graves, and bring you into the land of Israel. . . ." (Ezekiel 37:12)
The Bible teaches that the dead are DEAD, and do not go to heaven or hell at death, and that they do not have consciousness until the resurrection. As Solomon wrote, the dead know NOTHING (Ecclesiastes 9:5 - 6, 10)!
Babies are not automatically saved because they cannot understand nor choose to have saving faith. Although baptizing infants right after they are born seems spiritually comforting to the parents, it can't be seen as a practice clearly mentioned in Scripture. The apostle Peter told a crowd gathered in Jerusalem for the day of Pentecost to do something small children simply cannot do, which is to repent of all their sins, be baptized in the name of Jesus, and receive the gift of God's Holy Spirit (Acts 2:38).
Do babies understand and know enough about their sins to repent? Do they know who Jesus is in order to have saving faith in Him? Does the baby of an unsaved person (like an ignorant Chinese peasant) AUTOMATICALLY receive salvation until that child reaches a particular age? If this were true, then wouldn't it be BETTER for the child to die very young rather than grow up pagan (not believing in the true God)?
All those (including babies) who were never given a FULL chance to knowingly understand the truth of the Bible and repent WILL be given a chance to be saved (receive salvation) after they are resurrected at the end of the millennium (see Revelation 20:5).