General:
* Shivering
* Shuddering
* Rattling
* Thrashing
* Wriggling
* Spreading (water)
* Dispersing (water)
More descriptive:
* Vigorously shaking
* Energetically flinging
* Excitedly tossing
* Joyfully flinging (if the dog is happy)
* Exuberantly shaking
* Spattering (water)
Figurative:
* Water ballet (playful)
* Aquatic dance (poetic)
* Liquid acrobatics (impressive)
The best word will depend on the specific situation and the tone you want to set.