Adjectives ending in "y" can often be transformed into adverbs by replacing the "y" with "ily." In your example:
Adjective: "sloppy" (describing the dog)
Adverb: "sloppily" (describing the action of how the dog licked the food from her bowl)
So, it would be: "My dog was sloppy, and she sloppily licked the food from her dog bowl."