The dog who appears in this program is Pluto, the same dog who made multiple appearances on The Andy Griffith Show's S5 E6 Barney's Bloodhound and Dogs Dogs Dogs.
When Laura points out that if they set Horrible free he'll just be caught again, Robert says "If David Janssen can do it, he can do it." David Janssen is an actor best known for portraying Dr. Richard Kimble in The Fugitive (1963), who successfully eluded capture for four years.
The dog in question, a poodle/cocker spaniel cross, was called a 'poo-cock' in this episode. The crossbreed still exists under the name of 'cockapoo' (other variant names include 'cockerdoodle' or 'spoodle') and is quite popular; however, it is not yet recognized as a distinct breed by any major kennel club.