I had a Maltese before getting a yorkie and he was taken to the Vet 3 different times to keep him alive, 1. was a piece of pizza that dropped on the floor, 2. a piece of cooked chicken, 3. (My husband did it?) , a ham bone. The Vet said that small dogs have a very small pancreas and it could not digest any fat. That made me be so careful about Tricksie's food. I do give Tricksie cooked green beans that I chop and carrots, cooked or raw that is chopped in small pieces, but just a teaspoon.
She has never had a problem. BUT, all dogs are different.