It needs to have lots and lots and lots of extra room and pretty deep pockets. If he's going to stick with it for any length of time, he's going to acquire lots of mallets and sticks that are going to be all different sizes and length.
A shoulder strap would probably be helpful, and something to make sure that the sticks won't all fall out if it's turned upside down when it's closed is pretty essential.
You might look at stick bags online and see if any of them give dimensions.
Good luck with your budding musician! :D