Hunting any small game requires a hunting license for the state you are in and generally can be done only during specific hunting seasons. In nearly all states, non-resident hunting licenses are extremely expensive, so unless you have a a really big budget, you're limited to the state of your residence. The type of firearm you may use may also be restricted. The hike would also have to take place during the appropriate hunting season, generally in late fall.

Hunting is also a lot like fishing--if you rely on it for part of your food supply, you rarely catch any. Only if you carry a full food supply will you catch enough! The same is true of berry picking--if you rely on berries for part of your food, there will be very few available. Been there, done that, for both!

We do have a couple of Ohioans here who may be able to help on a location for a week's backpack.