How to Socialize with Other Pets
If you have adopted an adult dachshund and you have cats or other pets, you will want to determine whether your dachshund is willing to cohabit peacefully with these animals. Make introductions slowly with the new dachshund on leash. Never allow your dachshund to chase the other pet. Closely supervise all interactions until you are confident that your dachshund shows absolutely no interest. Even then, you may not be safe; the dachshund may just be waiting for the right moment to do some up-close investigations of her own!
Puppies, however, may be able to live peacefully with cats and other pets if they are raised with these animals and see them as legitimate family members and not pen-raised game for hunting. Again, even this approach is not foolproof. The movement of a cat or pet rabbit one day may be enough to awaken the dog's keen prey drives. It's always best to keep a close eye on your dachshund and err on the side of caution by keeping your pets separated when you can't supervise their interactions.
Other pets, such as rabbits, gerbils, hamsters, and such, are never really safe. Remember, the rabbit was one of the game animals that the dachshund was bred to hunt — and kill. It is better to keep the rabbits and pocket pets (and birds, too) safely away from your dachshund.