I can't speak specifically for the dog variety of the expression but in general the phrases along the lines of "... had the morals of a ..." are negative. Here are a few examples:
"Ferron was big, tough and ruthless—he'd break your arm as soon as look at you. He had the morals of a tomcat and the instincts of a rattlesnake."
"He was allergic to honesty, he bankrupted his family with inept business schemes, he had the morals of a stoat on heat and the maturity of a puppy, but Simon was a charmer."
"Markovites thought women were sinful, promiscuous creatures with the morals of a mink in heat."
"She had the face of an angel and the morals of a truck driver."
"She had the sweet trustworthy face of a baby-sitter, the morals of a ferret."
Edit: found one with a dog, sort of:
But how was I to know that Joshua would somehow manage to sneak in a keg of beer, and that Marlene Deitlemeyer, who had all the morals of a basset hound in heat, would kick over a lantern in the hay loft, whilst having a roll in the same?