Jesus delayed His until He was thirty. Adult believers were baptized after their confession of belief.
But not because His "confession of belief" was given Him from St. John or demanded of Him from St. John. In fact, His baptism was obviously not a believer baptism as He is the giver rather than the receiver of our faith, so if one wants to pattern the baptism after the baptism of Jesus, one would have to abandon the unbiblical idea of baptism as manifestation of faith already formed.
The baptism of Jesus is the sanctification of the Baptismal basin for of us. He never said "these waters are for adults who profess their faith"; but rather "it becometh us to fulfill all justice". Unless you are prepared to argue, with the Roe v. Wade babykillers, that "all justice" is bypassing babies, you have to admit that the baptismal font is for all men regardless of age.
And “entire households” we baptised as well. Did they include children? Most probably — though I’ll agree with you that it is ambiguous.