I finally obtained information about Bimperl/Bimbes/Bimpes/Pimperl the dog. From 1773 - 1777, the Mozarts kept a female fox terrier, called these four names by different members of the family. Wolfgang and Anna Maria usually called her Bimperl, Bimpes or Bimbes, while Nannerl and Leopold called her Pimperl. These are all various forms of the same name.
In 1777, Bimperl died and the Mozarts bought a male dog, giving him the same name. I found this information on the Mozart Forum.