So a household baptism offers no proof for infant baptism. Tell your preacher he will have to do better than that and actually give you a text that says babies were baptized. If he has been teaching you to baptize your babies, you have a right to ask him to give you Scriptural authority for it. So don't let him off till he finds it for you. But in that case not a word is said about their babies being baptized.
Infants are unable to believe the gospel.
And when Jesus gave the great commission to his apostles, as recorded in Matt. This shows that people must be taught the gospel before they can be baptized, but infants are not subjects of gospel teaching. If your preacher tells you that this says to baptize nations and that infants are a part of nations and should, therefore, be baptized, just ask him if infidels are not a part of nations too. Ask him if he thinks this authorizes the baptism of infidels. So I am begging you to ask your preacher about it.