This is a tough question for a lot of people, and it is made harder because there isn't a direct answer within the Bible. In spite of that, Dr. Ed Hinson and Dr. Ron Rhodes show us that we can find an answer by our understanding of God and verses that would apply to this question throughout the Bible.
Dr. Ed Hindson: There’s no specific Bible verse that deals with that, so we have to then ask ourselves, does the atonement of Christ cover children that are before an age of accountability or responsibility? And if you believe that it does, then you would naturally conclude that in the rapture He’s not going to leave them behind at that point.
Dr. Ron Rhodes: You know, I’ve done a lot of study on this as well, and I agree with Ed on that. Jesus had a special place in His heart for children. All you’ve got to do is read Matthew 18 to see that: “Let the children come to me.” We also learn that when children come into an awareness of sin and morality, that’s when they become responsible. And I think that we see that in James 4, you know, “to him who knows that it’s sin,” he becomes guilty at that point. And so I think up until that age that the child is not responsible. And I believe that at the moment of death the child goes immediately into the presence of the Lord if he or she should die. And it’s based on that same principle that I believe that the rapture will take them up as well.