I understand your thoughts here, but this is a statement to be very cautious about. Remember the flood during the time of Noah where everyone besides those righteous were damned and yes, that means all the babies, young children, and adults. We see from study who was left on the ark. This is a subject not well painted with a broad brush stroke.
The scripture has a decent amount of info about children and some were accountable at a very young age. If I am not mistaken the bible speaks of a 7 year old that became a king. To me I cannot even fathom that young of a person becoming a king. Now whether he had enough moral compass to be accountable might be questionable. If not, he certainly at some point did.
From the new testament (although specifically not stated) I tend to hold to there being an age of accountability for the young. I base that on the few statements Jesus made about the children. I certainly cannot prove that from Scripture so it is simply my perception.