In some cartoons Goofy had Pluto as a pet.
In Goof Troop:
The Goofs (dogs) had a pet cat named Waffles and the Petes (cats) had a pet dog named Chainsaw:
The Beagle Boys had a pet cat and a pet dog:
They live in a small tumbledown hide-out in Duckburg; in 1980s American-produced stories, their pet cat Ratty often lived there as well. In the Italian stories, they are sometimes accompanied by their pet dachshund, 64, who shares their criminal mindset, but it is often overcome with 64's constant, voracious appetite.
64 is the Beagle Boys' pet dachshund. Like his masters, he wears a red shirt and a green cap, marked with the number 64. The Beagle Boys frequently take 64 along on their robberies, to act as a guard dog and to reach spaces too small for the Beagle Boys themselves. However, the plans are often spoiled by 64's constant, voracious appetite. Whenever 64 smells food, he abandons everything else to get to eat it.
In my comic you have ANTHROPOMORPHIC cats and dogs vs. NON-ANTHRO cats and dogs. HUMANIZED and SENTIENT vs. NON-SENTIENT.
It is NOT that big a deal. They do it in cartoons all the time.
The issue I think is trying to figure out WHAT BREEDS the PET cats and dogs should be- should they be distinguishable breeds or some generic hybrids or mutts?