We don't do any of those things anymore. Yet we can be led to believe that we should beat a child with a rod. Christ came to establish a new law. When we think of young children as sinners we are in danger of setting up a self-fulfilling prophecy. They will grow.
Catholics baptize their infants.
Baptism cleanses the child of original sin. A baptized child, before the age of reason, is closer to God than any sinful adult can hope to be. He is living in a state of grace. If he were to die, he would certainly go to heaven. God did not choose to have a new soul come into the world as a miniature adult.