After reading your post (I love the comparison with dogs...I have never heard it put that way before.) and reading Jules' reply (which I agree is a much better way of looking at this.), I decided to add something also.
Another thing about becoming a new creature in Christ, which is what we trully are, is to always remember that God, our Father, can see the finnished product, the person we will eventually become. Not only that, in His perfect love for us, He CHOOSES to see us that way! Kind of like a parent who see's his baby child drooling all over the place, filling up diaper after diaper with, ummm, "fun suprises", and getting into things he isn't supposed to. That father loves his baby, even though it is quite a hand-full, and in his mind can "see" the man he will eventually become. Of course, God does it much better than that because what He see's is the real thing, He dosen't have to use His imagination!
At any rate, stick with Romans. Paul has a LOT to say about the subject through-out that book.
Love in Christ Jesus,