My dogs have also killed vermin, usually opossums or ground hogs. The squirrels on our property are the fastest in the county.
I figure that they're just dogs being dogs. I draw the line, though, when they start bringing their "trophies" into the house. One night, after I got the "kids" into the house and (I thought, wrong as it turned out) away from the possum they'd been hunting, one of the dogs dropped the varmint at my feet as she went trotting past me. Another morning I woke up to a dead ground hog in the house. Oh joy!
Every time they've done this, I toss the vermin over the fence. I most certainly hope that my kids don't start hiding their trophies in our furniture!
My husband remarked recently that in 2000 years when the archaeologists dig around our fence and find the bones, they will conclude that we 2009-dwellers participated in some strange rituals, judging from the animal bones . . . .