The short answer is probably not. We have taken on new students as young as 8 and as old as 70. So long as you are in reasonably health (kendo is a physical activity) you should be fine. Just make sure you inform us of any health issues you may have that could cause problems when exerting yourself.
For young children, it very much depends on the child.
Firstly, our weekday session might be quite late for some younger children (finishing at 10pm).
Secondly, very young children may have difficulty concentrating for 2 hours. While we accept children, we are not a children/juniors club and therefore our class structure is not tailored to making kendo fun for kids in the way it might be if we were. That's not to say your child won't enjoy it, our current youngest long-term member started training with us at age 8.