"I assume you know the difference between an animal developing a new characteristic and become an entirely new animal?"
Ok, but how many new characteristics before we call it a new animal?
That depends on which species concept you accept. The fact that no species concept has been universally accepted makes your challenge difficult, if not impossible, to defend.
Excellent question. Taxonomists fight over this question every day? What makes it a new species? What would put it in a new genus?
The fact is it's easy to classify things that already exist. Horses are different than fish are different than mold. And convienently there are very few organisms that push the boundries between designations. And the ones that do are fairly rare and hence given little concern. Is the duckbilled platypus just a freak, or did it go off on an evolutionary tangent, or is it surviving because it was fitter than an ancestor? We don't know yet.
Which incidentally is something that not many people involved in this debate are willing to say.... we just don't know yet.
How can you tell one animal from another? DNA? Could that be the answer?