While there's not a specific age that a child must be to become a Christ-follower, there are some key indicators that can help you discern if a child is ready or not.
Does the child understand abstract concepts? Normally a child can understand abstract concepts around the age of 7.5 to 8. In other words, the average four-year-old will think you mean a real bridge when you say Jesus is the bridge back to God. But when a child understands abstract concepts, they will grasp this as simply an illustration and will connect it to spiritual truth.
Does the child understand what sin is and realize they have sinned? Some call this the "age of accountability." The child must clearly understand that they have sinned and are need of a Savior. Before you can be "saved" you must first understand you are "lost" without Christ. The age of accountability is different for each child. For some kids it could be at age 6. For other kids it could be at age 9 or 10.
Does the child understand what Jesus did on the cross? The child should have a clear understanding of why Jesus came and the price He paid on the cross for our sins. The child should move beyond just "Jesus died on the cross for me" to understanding that Jesus died on the cross to pay the price of the sin bill we owe.
Does the child understand how one enters a relationship with God? The child should understand that we enter a relationship with God by asking Jesus to be our Lord and Savior. They should know we are saved by grace through faith and not by works.
Is the child persistent? A good sign that God is working in a child's life is the child initiating conversations about it. The child will begin bringing it up without being prompted.
Want vs. Need. Do you sense the child "wants" to make a decision or "needs" to make a decision. There is a difference. "Want to" can come from being coerced or by seeing other kids make a decision. "Need to" comes from a sense of the Holy Spirit's drawing.
Instead of doing large group "salvation prayers" invite kids to a class where you have time to clearly explain the Gospel and can talk with them individually. Have parents attend the class with their children. It is vital to partner with parents during this process. And the cool thing...as you do this you will see parents come to Christ as well.
When a child begins asking questions about following Christ, it's an exciting time. What a privilege we have to share Jesus with children. But we also carry a responsibility to help children understand what that means.