I am willing to bet that there is some GSP (German Shorthaired Pointer) in her.  When you described how much she likes to run and the way she sniffs and "hunts" you could have been describing my Morrison.

I'm not really familiar with MinPins but GSPs are really common here in MN and most of them have the dewclaws and tales docked just like your girl.  They way her ears fold back also reminded me of Morrison's "flying nun" look.

Whatever she is she is very pretty and good for you for giving her the excercise she needs!