You did not work for her or her business in any capacity so you are not required to fill in a W-9 or is she required to send you a 1099. What is her business? Is it a pet store ? Sadly it sounds like she is trying to justify a personal expense as a business one.
You simply sold her a puppy which is no different than any other business supply would be for instance paper or ink. You should have issued her a receipt for the purchase ... part of the receipt came from Paypal and the rest you should have sent her some kind of invoice.
