Rabbit or squirrel. Would say no on the coon dogs. I run hounds and love coon hunting but for little kids it isn't the best introduction to dogs and hunting. Being at night, most of the good hunting is when the little ones need to be sleeping. If she's tired when you start and you keep her out late she won't get near the enjoyment that she should. Also done along creeks and rivers. You get wet and often times cold. Better to indoctrinate them to coon hunting when a little older IMO.
You also run the risk of the dogs catching a coon on the ground. Doesn't happen often but when it does the fight is on!!! That could be a traumatic experience for a little one.
Never hunted rabbits or squirrels with dogs but beagles make great family pets and those that I have talked to that have been have really enjoyed rabbit hunting with them. I would recommend hooking up with the preacher, getting a beagle and doing the rabbit thing.