If I was given a puppy as a gift, and now the purchaser wants it back, who is the legal owner?

My (newly) ex-roommate decided to give me a puppy for my Christmas gift. She constantly bragged (in public) to my friends about how she was giving me this puppy. There are about 15 people who heard her say she bought the dog for me. (If she takes me to court, will their statements saying they heard her say the dog was a gift help my case?). However, now, she is threatening to file a case in small claims court. I am/have paid for the dog's most recent vet bills and other necessities (dog food, toys, etc.) and the dog has been under my care since she moved out. However, when she left, she decided to take the dog's AKC registration paperwork (which at the time had not been filed). She ALLEGEDLY filed his registration paperwork. She is now threatening to file a claim for custody of the dog, but I feel like the dog is mine because it was a gift and I pay for his expenses. Does she have a case or will the court decide that the dog is legally mine?