I've reviewed what folks have posted above and it's fairly complete but you've sadly neglected the nautical dog songs:

"The Irish Rover" (and the poor dog was drowned...)

"The Dogger Bank" (Nothing to do with dogs)

"Sea Dog" (nothing to do with dogs)

"Bull Dog Don't Bite Me" (Barrouallie Whalers)

Cheerily,
Charley Noble