There are a bunch of dogs in this novel. There is Sandy, the narrator's dog; Spot, a (sadly deceased) dog of Billy's; and Princess, the freezing-cold German shepherd who accompanies the soldiers that capture Billy and Roland Weary in the cold forests of Luxembourg.
These dogs appear briefly, and we don't want to read too much into this, but it does seem significant that, when Billy is on the run from the Germans in Luxembourg, he sometimes hears dogs barking. They indicate that the German troops are nearby and the sound is terrifying. But up close, all the dogs we meet in the book are loyal and likable. Even Princess, an imposing German shepherd, is just a frightened animal, cold and unfamiliar with war. Again, Vonnegut hammers home the point that appearances can be deceiving