And “entire households” we baptised as well. Did they include children? Most probably — though I’ll agree with you that it is ambiguous.
According to The Bible, parents, including Jesus' parents, dedicated their children to God. This was a way of agreeing with The LORD know that their children belonged to Him, and they were dedicating themselves to raising their children as His. All the Jews, including the ones who had Jesus crucified were as babies dedicated to God, so it is plain that dedication did not automatically save them. If they had been truly saved they would not have had Jesus crucified. Jesus would not have told many of them that their father was the devil.
The Bible says that when King David's baby died shortly after he was born that the child was in heaven. If a child dies before the age of accountability it is taken to heaven, by the sheer and utter mercy and grace of The LORD. Somehow He is able to apply Jesus' sin cleansing blood unto a child who dies, because the child is yet without accountability.
Heaven is likely full of children. Just think of all the children, from the beginning of time, who have died in the womb, or of starvation in third world countries, or have been too weak to make it having died early, or have been not wanted by heathen parents and set aside to die, or have been aborted. When Jesus said "for such is the kingdom of heaven", He may well have been referring, at least in part, to how very many children are up there.
Mark 10:14 But when Jesus saw [it], he was much displeased, and said unto them, Suffer the little children to come unto me, and forbid them not: for of such is the kingdom of God.
Mark 10:15 Verily I say unto you, Whosoever shall not receive the kingdom of God as a little child, he shall not enter therein.
Mark 10:16 And he took them up in his arms, put [his] hands upon them, and blessed them.