The New Testament speaks of the
baptism of "whole
households" which in the
normal Greek usage of the time
included children.
1 Corinthians 1:16
I (Paul) baptized the household of Stephanas also ...
Acts 11:13-14
He related to us how he had seen (the) angel standing in
his house, saying, 'Send someone to Joppa and summon
Simon, who is called Peter, who will speak words to you
by which you and all your household will be saved.'
Acts 16:15
After she (Lydia of Thyatira) and her household had
been baptized, she offered us an invitation...