Someone reading this may ask, “Why in the world would anyone even consider such a horrible notion?” I “googled” the question out of curiosity and got 117 million hits. Most responses to this question are emotional but not necessarily scriptural.
If you believe that life begins at conception, and a baby dies (aborts) before birth, then you have to add the unborn to this question. They are not baptized. If you believe that innocent children can be delivered into everlasting damnation, you’re worshiping a monster, not God.
Centuries ago, Catholic priests concocted this doctrine of devils (1 Tim 4:1) to scare ignorant folks into staying faithful to the Mother Church. The prospect of their baby roasting alive in the fires of hell for all of eternity was sufficient motivation for parents who didn't know what the bible said. Today, people do know better, and the Catholic Church avoids the subject, even though they continue to promote and practice infant baptism.
For a more thorough discussion on baptizing children, read this article.