I don't think anyone can argue that the .22 is a great round for dispatching game/slaughtering livestock, but that doesn't necessarily make it a good SD choice.
I'd repeat what someone else already said about trying a lighter shooting 38spcl first. Or try a sp101. They weight about 14lbs and as such soak up far more recoil than the air-weight j-frames.
That being said if all she can handle is .22 it's far better than nothing.
I'd go with one of the j-frame size Tauri - or one of the S&W's if you can find it. I definitely think that with rimfire you'd want to go with a double action revolver. If you have a misfire, just pull the trigger again.
si vis pacem para bellum