Sorry to hear about your TV! We hope the dog is sorry, too.
The good news is that TVs are normally covered by renters insurance, along with your other electronics, furniture, clothing, art, and other possessions. However, it must be a covered peril for the damage to be covered. Unfortunately, accidental damage is not usually covered.
Before you file a claim, here are a few things you need to know about TV damage and renters insurance: