Logically speaking, that isn’t the case at all. There were no baptisms here of the children, while Jesus (through His disciples) baptized people. And Jesus’ statements on children make the point that they are acceptable to God. He held them up over and over to say, as He did, to adults, that they must be born again and become as little children to enter the Kingdom of Heaven.
There is no way to rectify the term ‘whole house’ with an exclusion of children below a certain age.
You have a large square peg that simply will not fit into the round whole demanded by reality.