Is it explained in one of the other works why Abby couldn't follow the Cullens' example and just drink animal blood?
In the book Undead Håkan does do some killing of some cats that he may have also drank blood from in the process but we only get the aftermath described on page not the actual event.
There's also some discussion in a couple instances that quality matters to the blood. Hakan has to take the blood while the victim is still alive, Eli gets into a short drug induced state when she drinks someone on heavy medication, etc. So it seems a logical extension in-universe that animal blood might not be quality enough to sustain Eli's hunger.
There's also the problem of zoonoses: animals being possible disease vectors to transmit diseases to humans. Obviously being a vampire, in this universe, makes you immune for human infectious diseases, or they could never have continued to exist; but who says that that immunity extends to animal infectious diseases, like rabies?
