None of them really as it was only a dog - and all of those alternative words require an awareness of wrongdoing.

However, in general

culprit - need not be a serious situation (as in your example) but means 'the person/animal responsible for doing something bad'. It can be a very minor bad thing.

sinner - this is someone who breaks a religious 'law' and it's only appropriate if you are discussing within a religious context. Although some religions would hold that we are all sinners, plenty of people do not believe in the concept of sin at all.

criminal - someone who has broken the law

wrongdoer - someone who has done something wrong but it sounds oddly archaic/formal to me.