Why are Dorothy and Palmer certain they must get Nipper out of town? What other options do they have?

Both Dorothy and Palmer believe that if Nipper stays near Palmer, sooner or later Beans will catch up with the bird and kill him. No matter what other ideas they come up with, including hiding Nipper at Dorothy's house, none seems to solve the problem. They are both certain Nipper will die at the hands of Beans unless they relocate the bird.