While you can get some freezing with speeds around 1/300 (see the first photo below), I would recommend going with faster shutter speeds if you want to take shots of water drops falling or moving away from wet dogs.
One thing to keep in mind is that most flashes have a limit on their sync speed, which means that the use of flash will limit your fastest shutter time available.
- Example 1: 1/320 speed, no flash:
(as you see there's still blur on the water and a flash, even if able to reach the dog, wouldn't make much a difference if it wasn't able to go faster than 1/320)
- Example 2: 1/1300 s, using the internal flash of a Panasonic FZ18 and the ambient kitchen light:
Here a smaller aperture and the ambient light allowed for a slight slower speed, but the shot is sharp enough for me.
- Example 3: 1/1600 s, using the internal flash of a Panasonic FZ18, no ambient light (shot in the dark):
Here the speed was enough to freeze the drop and the flash was set stronger enough to provide the needed reflections on the background (since there was no ambient light).
Finally, if you are into capturing water drops don't miss John Cavan's very good post on the subject - Catching the Elusive Water Drop