The best mouse, mole and rat killer we ever had was our miniature dachshund who was bred to be a sporting dog in Alabama. He used to come back with a "gift" for us far more often than any cat that we have ever owned. Since he got old and died we have had a terrible problem with moles.
Yep, dachshunds are good ratters. In fact, I think that is why so many pet daschunds are “high strung” and jumpy, nippy little things. They were meant to be worked daily to burn off all that energy, but when kept as lap dogs they have no outlet for it.