For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Acts 16:14-15 (NIV) One of those listening was a woman named Lydia, a dealer in purple cloth from the city of Thyatira, who was a worshiper of God. The Lord opened her heart to respond to Paul's message. When she and the members of her household were baptized, she invited us to her home.
Acts 16:31-34 (NIV) At that hour of the night the jailer took them and washed their wounds; then immediately he and all his family were baptized. The jailer brought them into his house and set a meal before them; he was filled with joy because he had come to believe in God—he and his whole family.
Matthew 18:2-6 (NIV) He called a little child and had him stand among them. And he said: “I tell you the truth, unless you change and become like little children, you will never enter the kingdom of heaven. Therefore, whoever humbles himself like this child is the greatest in the kingdom of heaven. “And whoever welcomes a little child like this in my name welcomes me. But if anyone causes one of these little ones who believe in me to sin, it would be better for him to have a large millstone hung around his neck and to be drowned in the depths of the sea.
Whole families were baptised, and causing a little believer to stumble is a serious crime. Why would we refuse to baptise those granted baptism by the Apostles?