Hi!

First first first first--get the battery or batteries out of the camera!!
The sooner you do this, the better for everything involved.

Second--remove the memory card from the camera and look for any backup
batteries. Since it fell into a dog bowl, putting it into a bowl of clean
distilled water might be a very good idea to help flush any crud out of it.
You can't make things any worse at this point.

Third--Dry the camera as best you can. Then put it in a moderately sunny
place or somewhat near a heat vent. Let it rest for a few days.

Fourth--put the battery back in and you might get very lucky. If the camera
doesn't work at that point, you are probably out of luck. The key here is to
get the battery or power source removed as soon as it is possible to do so
safely.

William