The whimpering tells you that this dog is hurting bad. It limped up behind you when you sat down for a rest. Now it won't leave. Cute dog, though.
1.Do what you can for the dog. Use the rags and that standing water over there. Maybe he'll make it? (Spoiler: He snaps and runs away. Nothing happens.)
2.Give him a pat and leave him behind. You don't need a dog. (1 dirty rag, 1 water)
3. Crippled dogs aren't any use to you. Throw rocks until he limps off into the distance. (1 dirty rag, 1 water)
4. He might be crippled, but there's enough meat left on him for a decent meal. Kill, gut, and skin him. Looks tasty. (2 small chunk of meat (cooked), 1 medium chunk of meat (cooked)
1.There is currently no way to get the dog, even with the medic trait. :(