Cool dad to work with your son on projects. I recommend using this for further learning. The first go round works, but has some problems.
The 9V does not have much capacity and the project uses power even when on. Brain storm on how to improve that.
Since going to a simple resistor, switch, and battery would sort of be going backwards how about figuring a way to do the same thing with component or more simple logic chip. What you have is a flip flop circuit.