At that age I think my pup was too frightened to go outside by himself! Then again, he's still afraid of the dark

Apart from the safety aspect, you are your pup's Dad. Pups need to be taught what is right and wrong- if it picks up stones, you need to be there straight away to say NO. Same goes with eating poo. It's quite natural for dogs to eat their poo and very common, but once they have started it's very hard to make them stop. I like to watch my dog poo (that sounds weird, but bear with me) so that a) I can see whether it's all good and healthy poop, nothing dodgy in it b) to stop him eating the stuff and c) to pick it up.
Mav is about 4 1/2 months and I will let him out to go to the toilet but will stand near the door, I'll let him out whilst I do little bits and pieces like boil the kettle, put the toaster on etc, but make sure he is within eye and ear shot at all times. If I'm going to be distracted at all, he comes inside, if I'm going for a shower or engrossed on the phone he goes in his crate because I know he's safe there.