He's way too small for those collars.
Build a small fence (you can also buy a puppy gate) and put it in front of the door
In case the dog gets out he can't get far !
Teach the child to never open the outside door without speaking to you first, then the dog won't go out, I have a little sister she was 2 years old when we got Fido, we never had a problem with him getting out, only about once or twice, but that was kind of my own fault.