Have you tried "care credit"? It is a medical only credit card of sorts. We have a dog with an auto immune disorder, and getting her diagnosed was quite costly. You can get a 3 months, no interest deal, too.
Has the dog been diagnosed with anything yet???
I know when my dog was having issues, I googled her symptoms and read absolutely everything I could get my hands on. We finally had to get a biopsy done to get a true diagnosis.
Good luck. Here's the link to care credit. Let us know how it goes.
CareCredit® Healthcare Finance - Payment Plans and Financing for Cosmetic Surgery, Dental, Vision, Hearing, Veterinary & Other Medical Procedures