Asics Patriot 13 GS is an excellent running shoe for junior runners. The shoes have a solid EVA foam in the midsole that protects against impact from the ground and feels energetic. The upper part is made of a ventilating and supportive material that keeps the foot well in place - there are also both laces and velcro closures, so they are easy to get in and out of. 

If you need a sensible running shoe for your child, the Asics Patriot 13 is certainly a good choice.