You can't blast or shoot the dog in any way. That's illegal.
Additionally, you may not be able to even pull your trigger or aim your gun when the dog is sniffing around, and every time anything flies on the screen, the dog is invincible to any kind of projectile. Furthermore, you have to stop and relax for 2 seconds after you've shot down your targets as the dog picks them up for... whatever purpose.
There's even the conspiracy theory that says that the dog actually decides whether or not your shots would hit as he would sometimes (or all the time) be seen laughing whenever you can't hit anything.
The dog also prohibits you from sitting too close to the TV, and therefore, you cannot hit anything if you try to aim your gun at point blank to the TV.