Well, some authors have made sure that their favorite animals don't get overtaken by zombies, but survive and help protect their beloved humans, or some play other roles in the story. Here are a few zombie books with pets that I came across, some you may know and some may be new to you (and me):
The Book Of Riley ~ A Zombie Tale by Mark Tufo, (the first of 4 books), American Bulldog Riley tries to keep her pack--a high-strung Yorkie, her favorite "two-legger" Jesse and his younger brother, and her arch-enemy the cat--safe as they depend upon each other to stay alive. (86 pgs.) (Also in audiobook)
Pet Sematary (one of my favorites) by Stephen King is of course the definitive love story gone wrong when a beloved pet is buried in a haunted cemetery (and doesn't stay there).
In Zombies, Cats and Heroes by Brett A. Fernau (who appears to be an avid cat lover with a selection of different books featuring cats), a man and his cat find a way to reestablish civilization in the face of a "mind virus."
Girl Z: My Life as a Teenage Zombie by C.A. Verstraete, one of 16-year-old Becca's greatest fears comes to light when her uncle brings over his big German Shepherd dog, Chico. Becca, of course, wants to make sure her Tia Imelda is safe, but she has a particular (unfounded) fear about dogs as seen in this excerpt:
I love dogs, but I still wondered . . . "Carm?"
"Will, you know, the dog hate me?"
"Hate you? Why?"
"You know, because I'm, uh, different? I must smell different, don't you think?"
Carm stared at me, then glanced away, but not fast enough for me to miss the flash of guilt. "Well, maybe. You do, um, kind of smell a little sometimes."
Her comment made me jump like she'd stabbed me. "Wh-what? You-you mean I'm starting to smell like-like . . ." I gulped. The idea repulsed me. "Like one of them?"
Carm gave me a sheepish look before she answered. "Bec, I didn't want to say anything. But don't worry. You're nothing like them. It's only a little. A real little. It's hardly noticeable."
"Uh, ah, it's because I'm by you all the time," she sputtered. "Don't worry about it."