What would it take to kill a squirrel, rabbit, or even fox with a 6mm bb?

If your gun can shoot through both sides of a condensed milk can it is powerful enough for small game. It will still require a well placed shot. The 1000 fps will generate enough energy for a very close range fox with a well placed shot behind the ear. My advice is to get a 22 magnum. Cheap to shoot and powerful enough for dog sized animals.