There is a reason to hunt with the calibers you use for self defense.
On appropriately sized game, it is the best "real world" demonstration of the terminal ballistics you can expect of your SD rounds. Granted the range will generally be far outside those encountered in a SD situation, but it will show the very minimum you can expect.
Using the same handgun you will be carrying will also tie the results to the actual weapon you will be deploying.
Your choice might not be the best combination for hunting, but it will be the best combination for evaluating your carry weapon.
Will you hunt with "ball" or one of the hot shot SD ammo available?