You in Ok.
Have hunted dogs for nearly forty years, from rimfires to medium bore centerfires, and once, very judiculusly, airguns. It's simply poor ethics.
I've had dogs make it down thier holess with two feet of entrails dragging behind them. And yes, it was a bad shot. But anybody who says they don't occasionally botch a shot is somebody I wouldn't hav in my house.
If you can headshoot them every time, you bet, go to it. But to body shoot them is pure and simple bad sportsmanship. I hope you reconsider your hunting ethic before the next hunt. Varmint or not, they still deserve our respect and a humane dispatch. You simply can not do that with any airgun unless you're right on top of them.
Suggestion; don't try to bull***t an ole' bull******r.
badshotlal