A person should be old enough to understand what is right and wrong. He should be able to make a decision to give his life to Christ. Many children are ready for baptism at 9 or 10 years of age. Some children are not ready to be baptized when they are 12 or 13. The Bible does not give an age for baptism.
Children have different levels of understanding and maturity.
Some children are ready for baptism earlier than other children. But if a person refuses to be baptized, he is disobeying God. There is one sin I do not want to give up. You are not ready to be baptized because the old life of sin is not dead. A funeral director would not bury someone that is not dead.