I think we could have done without the close up photo of your dog's poop, but first of all, it's against Airbnb terms of service for a friend to book for you- the person booking has to be among the guests staying. And it was your and your friend's responsibility to make sure you were aware of, and didn't violate the host's house rules. If you are planning to travel with your dog, you need to make sure it's a pet-friendly property.
That said, what exactly is the host saying that $1500 they are asking for is for? I can understand asking for extra cleaning fee and maybe a fine for ignoring the no pets rules, but I agree that $1500 is extortionate, unless your dog destroyed things in the home. I think the host is just really pissed off that you came with a dog and if I were you, I wouldn't be arguing about whether it was my dog's poop or pee- that's just juvenile. You don't have to pay more, and you can ignore the host's threats- I really don't think anything will come of it, but please, in the future, book under your own account and don't bring a dog to a no pets listing.
@Austin21