I would say go deer hunting whenever you want. I don't really see why you would start out small and then work your way up. It's not like you're leveling up a video game character.

Not that it matters, but I started three years ago on deer (also in KY), then moved to turkey, then rabbit and squirrel and groundhog, with coyotes spread in there somewhere after they started eating my birds. I don't really see any experience in the smaller game that would have "prepared" me to hunt deer more effectively than just hunting deer did. Similarly, I don't feel that a great deal of the deer hunting experience has enriched my ability to hunt the little things.

As others have said, though, hunting with this friend of yours might be the biggest detriment to any hunt.