The net force on the wagon is not zero. If the child pulls with a force F (where we set our coordinates so that "forward" is positive), then the force on the wagon is +F and the corresponding force on the child is -F. If these were the only forces operating (say, if the child is on a surface with ~zero friction, as if they were on ice skates), the wagon would accelerate forward, and the child would accelerate backward.

But these are not the only forces involved. In particular, the child is pushing on the ground. The ground exerts a force back on the child - let's call it A for "anchoring" - in response. So the total forces are:

• The wagon experiences a force +F from the child pulling.
• The child experiences a force -F from pulling on the wagon and a force +A from pushing on the ground.
• The ground experiences a force -A from being pushed on by the child.

These forces do sum to zero, satisfying Newton's third law, but the forces on each object do not (assuming F and A are not zero, the child is the only one who could be experiencing zero net force here if A and F are exactly equal).