It's not all about punching and kicking. The most useful thing you can teach a young child about martial arts is how to execute a proper break-fall.
A break-fall is a method used to minimize the risk of injury when falling to the ground, and it is easy to do, with practice.
The above link is an example of how the move is executed during sparring.
When practicing a break fall with your child, it is best to use your bed or a blow-up mattress, so that you can avoid pain if and when a mistake is made, and so that confidence can build when executing the maneuver. It is imperative, though, to explain to your child that the move won't make it so that falls don't hurt, but that they can prevent injury and major "boo boo's".
To practice, start in the standing position. Choose which way you are going to fall (on left or right side). Turn your head in the opposite direction, bend the knee of the opposite leg of the side you're going to fall (so that the foot is off the ground), and let yourself fall to the side chosen. Upon impact, extend the impacting-side arm, and ensure your hand is open, so that you can "slap" the ground. To practice the move falling backwards, tuck your chin into your chest, extend both arms, and fall, similarly "slapping" the ground. Practice the move on each side and backwards multiple times, and watch your child so that you can monitor the accuracy of their execution.
When practicing all sorts of maneuvers in the military, we used sayings, or "ditties", to help remember what to do. For this exercise, an example of a ditty would be "turn the head, lift the leg, and slap the ground". You can use any ditty you can think of to make the move easier for your child.
This move is great for all sorts of situations, from falling off the jungle gym to losing balance during playtime. With practice, it can become second nature, and you can feel comfort in knowing you have minimized your child's risk of serious injury!