Quail shouldn't mind, but I'm not too sure how effective it'll be against rodents. Worth a try, though, I suppose. It might stop them from smelling the quail feed and knowing it's in there to get at.
Just a warning, though: mint escapes. So much. It will get out of anything you put it in, including a pot with a drainage hole that's set on top of dirt. Resign yourself to having to mow over escaping mint if you have a lawn. My neighbor has a mint patch that's edged by their house on 2 sides and the sidewalk on the other 2 sides, and the mint has gone underneath the sidewalk via its roots and popped up on the other side. An 18" deep barrier of something it can't go through would hopefully keep it in, but it'll escape just about anything else.