http://www.rrrrthats5rs.com/games/dont-shoot-the-puppy/
The entire point of the game is to NOT shoot the puppy... Also, to not fall for trick after trick that would trick you into shooting the puppy... I'm on level 13, so far... I've only fallen for it once (early on, level 3 I think)
Give it a try. It's a game of patience and basically being suspicious of everything...