Yes, thanks for catching that.
Actually, the same goes for your argument as well. My arguments states: "Whole households were baptized, so one would expect there were young children/infants in those households"; while your argument states: "Whole households were baptized, so one should not expect there were young children/infants in those households". Both of us are making the same type of argument, just one positive and the other negative.
So from the perspective of baptism to get to an explicit answer from Scripture, one has to ask the questions: "What does baptism do?" and "Would whatever baptism does be beneficial to infants and young children?" and "If there is a benefit to infants and young children, what would be the reason from restraining them from those benefits?"
Obviously those questions are outside the scope of this thread, but from the side of all Apostolic Christians the answers are: "It confers the Spirit of adoption, justifies or reconciles the person in the eyes of God, removes all sin (both personal and original)"; "Yes"; and "No reason".
Now one of the things to remember as well, the book of Acts speaks about the Church as it is growing. There are no second generation of Christians mentioned in Scripture, so the Bible is silent on the matter of how to handle the next generation of Christians. Rather what we have is Sacred Tradition to answer that question.