It wasn't a single cartoon but a series of cartoons featuring Tex Avery's signature brand of wacky humor. Two recurring characters in these cartoons were "Droopy" the dog and "Wolf", his nemesis. While the name "woofer" and "whimper" aren't explicitly used in the cartoon, it is possible you are remembering their vocalizations which are characteristic of these characters.
Droopy is known for his slow, deliberate speech and his ability to always outsmart the wolf, who typically has a loud, raspy voice.