You may believe that church authority was equal to the authority of the Bible, I do not.
It was the "Church authority" that chose the canon of the Bible you are using, and that was a highly contentious decision in the 4th century that took over a half-century to finish, and even over that time they were indecisive when it came to what we now call the "Apocrypha". Jesus said that he would guide the Church until the end of time, and Pentecost was one manifestation of that promise and is considered the "birthday" of the Church. And Paul said that we should follow the traditions that they left us, so not all was written that happened.
The Philippian jailer account doesn't mention babies. and if it did have babies, that means that Paul and Silas would have had them woken up in the middle of night and preached the word of the Lord to them. Read the account again.
Generally speaking, back then what the father was the rest of the family also was since Jewish and early Church society was highly patriarchal.
Either way, the issue really is far less important than one may think since baptism does not involve forgiving any sins beyond the sacrament/ordinance itself. IOW, it's a means to an end, not an end in and of itself. Also, the element that is missing in infant baptism, namely belief, is made up in the sacrament of confirmation.
So, if you and your family don't believe in infant baptism, then maybe don't baptize your infants; but for those who do believe in it when it's matched with confirmation, I would suggest that this is their choice and is a rather logical one at that.
Finally, no church today is an exact replica of the early Church in terms of their practices. For example, do your women keep their hair covered in public? Are they silent in services? Does your church choose your leaders by drawing lots? Do you greet each other with a "holy kiss"? etc?
The Church has always been dynamic, not static, which is undoubtedly why Jesus said he would
guide the Church. And a static church would need no guidance, so all churches make decisions on what they think is right.