The opposite could also hold true. The text does not say there were no infants therefore, your post above assumes that there were no infants.Acts 16:31 is the only scripture offered in defense of infant baptism in the above so lets notice a few things in its context.
1. The text DOES NOT say infants were included in the jailer's family.
2. Therefore it must be ASSUMED there were infants. Assumption is a poor method for establishing a cardinal doctrine
of a church.
If we take this part of Acts 16 at face value what can we determine? What does "all his household" mean? It does not say all those above a certain age or understanding. What we know from this text is that to be saved one must believe. It says he spoke the word of the Lord to all in his household. It says that all in his household were baptized. It does not say that all in his house believed. It does not say all those who were baptized were saved.
Then he called for a light, ran in, and fell down trembling before Paul and Silas. And he brought them out and said, “Sirs, what must I do to be saved?” So they said, “Believe on the Lord Jesus Christ, and you will be saved, you and your household.” Then they spoke the word of the Lord to him and to all who were in his house. And he took them the same hour of the night and washed their stripes. And immediately he and all his family were baptized. Now when he had brought them into his house, he set food before them; and he rejoiced, having believed in God with all his household. Acts 16:29-34 NKJV