I spoke to a guy years ago who was deported. He was able to spend about three months in Canada before the mounties caught up with him (his only lawbreaking was illegal entering/staying). Anyway, they took him directly south to the nearest crossing and handed him off to U.S. Customs, who I am sure ran him before releasing him.
...as for your dog, I am pretty sure The Canadian authorities want him/her gone too and will deport both of you. Not sure how it will go if your dog's paperwork isn't in order when trying to re-enter the U.S.