Baptism is for believers. An infant is incapable of making a profession of faith. First what is it? Baptism in the ancient was much like an altar call is today. Once one makes a profession of faith they followed that with a public profession and baptism. Phillip and the Eunuch is a great example. After Peters sermon was another.
If Paul baptized kids I would need to see the verse. Vizion you said Paul baptized households which is true. The Philipian Jailer was an example. However it does not mention infants or kids for that matter. What it does say however is that he p[reached they believed and were baptized, Acts 16:31-34 So in this case it is clear that it was a believers baptism. I would need to see a verse that in its hermeneutic context shows any infant baptism. Then we can discuss it in more detail. I am u aware of any such verse but there are countless verses that show believers baptisms. Hope this helps sir.