When are we accountable?
Determining at what age an individual becomes spiritually accountable for what they think and do is IMPOSSIBLE for humans to determine. This is because only the Father knows the intentions of a person's heart and what they believe and understand. For a person to have a belief, there must be some understanding of what is to be believed (see Mark 1:14-15).
To repent a person must have an understanding of what they are repenting of and what is the gospel. During one of his missionary journeys the apostle Paul and Silas were thrown into jail. While they were singing hymns at night a miraculous earthquake occurred that not only freed them from their shackles and cell but also broke the chains and opened the cells of ALL the prisoners! The guard of the prison was in such awe of the miracle that he ran to Paul and Silas, fell down before them trembling, and asked what would it take for him to become a Christian.
'Sirs, what must I (guard of prison responsible for all the prisoners) do to be saved?' 31 They (Paul and Silas) answered, “Believe in the Lord Jesus, and you will be saved - you and your family.' 32 Then they preached the word of the Lord to him and to all the others in the house. 33 At that very hour of the night the jailer took them and washed their wounds; and he and all his family were baptized at once. (Acts 16:30 - 33)
Note that the guard and his household had to understand and believe in the Gospel FIRST before they could be baptized. Peter state these steps of repentance THEN baptism in his well-known message on the Holy Day known as Pentecost (Acts 2:38).
What is needed for TRUE repentance?
Until a person becomes old enough, they do not have enough understanding to fully repent of their sins, begin to obey God, and with full knowledge of the consequences of their actions, be baptized. They also do not have the emotional maturity to deal with the sometimes narrow and difficult road a Christian must travel in this life. You can read the Bible from cover to cover and you will NOT find any example of babies or young children receiving baptism (as the Catholic Church promotes). Those who die in this life without receiving a full chance at salvation, no matter what age they are, will someday be resurrected and given the opportunity to receive eternal life.