I would definitely hold off on the regular whole milk until as long as possible (for various reasons, see below). But since you state that he does well with yogurt and cheese, the transition to whole milk should be pretty smooth. But transition slowly, especially since he is only used to breast milk. Start slow. Mix only breast milk with the oatmeal for like 2-3 days, then move to 3 parts breast milk to 1 part whole milk. Do that for 2-3 days. Then 2 parts breast milk to 2 parts whole milk for 2-3 days, and so on, until you have transitioned him to only whole milk.
Good luck!
(PS- If you are open to natural/alternative milk methods (which are MUCH easier on baby's belly), send me a private message! I would love to fill you in!)