I believe young children can and do have conversion experiences before the age of 13, and Baptism should follow.
I think the concern with the age limit is that some kids go down to the front, not because they want to know God, but rather they want to be a part of what is going on in the church (e.g. following what a friend or another family member is doing). In that case, a child from a semi-involved church family may believe his salvation is taken care of, only to realize later in life that they did not know what they were doing at the time and need to re-commit their lives often with a second baptism.
Typically there is little difference in the 'I got it right at age 9' and 'I went down too young, and re-dedicated later'; it's not like we know everything about the working of the spirit, if you are pre-destined, God will be calling you your whole life, and you will be on your spiritual 'journey' from a very young age anyway.
The main concern would be the exception: a young person goes down front at a very young age, does not understand what he is doing, strays as a teen or young adult, and never understood what becoming a christian means. The conversion experience (or submitting to the Lord) was never explained well, and they go through life thinking they are christian, but have no real relationship with God, or submissive heart. But, these individuals may not have faired any better by waiting until they were a little older, in fact they may have faired worse! But, perhaps, if the parents are involved, and help the youngster understand, it will all work out in God's time, and no magical age limit need be applied.