Is it permissible to pray in the shirt shown in the picture?

Prayer is not permissible in clothes bearing images of an alligator or any other animate being. However, the prayer itself is valid, though sinful, because wearing clothes with images of animate beings is forbidden. There is no difference in this ruling between an adult man and a child.

The Prophet, peace and blessings be upon him, became angry when he saw a curtain with images and tore it down.