I know of nowhere in the Bible the specifies a particular age as the point in time when a person is considered accountable.
My assumption is that "accountable" really means "responsible for a decision regarding Jesus Christ as Savior." In my understanding, before this point, the child would go to heaven if he or she died.
You may wish to see my sermon which deals with this (The Death of David's Son):
This age of accountability applies to the so-called "heathen in Africa" as well. They do not know about Jesus, but they are condemned for rejecting what God has revealed of Himself in creation (Romans 1:18ff.; see also Psalm 19 and Romans 10:18). You may wish to see:
I would understand that there is a point in a child's growing up when they are accountable for their decision regarding what God has revealed. The best place I can think of is in Jonah chapter 4, verse 11:
11 Should I not be even more concerned about Nineveh, this enormous city?
There are more than one hundred twenty thousand people in it who do not know right from wrong, as well as many animals!" (Jonah 4:11, NET)
If a child is not able to discern between its right and left hands then it is not yet old enough to be held accountable for a decision regarding the salvation Jesus has provided. (In my opinion, this point in time may differ from one child to another, and thus it is known only to God.