The typical homeowners' coverage form excludes animals from items covered under personal property. I have never seen a homeowners' policy without the exclusion. Some carriers do, however, offer some limited coverage for pets as part of an enhancement endorsement. You should research what your carrier offers if you haven’t done so already.
There are pet mortality policies available, as well as coverage for the pet’s medical needs that are similar to health insurance. These are offered by specialty markets.
ISO and AAIS homeowners' coverage forms exclude damage or injury to pets and the great majority of insurers closely follow this practice. However, I have recently heard of a few homeowners' policies that may provide very limited medical coverage for certain pets owned by the insured.
It depends on the policy form. Although a pet is personal property, many forms specifically exclude fish, birds, and other animals from covered property. Some might have a special provision to cover domestic pets injured or destroyed by a covered peril. If it’s a special pet, then consider obtaining an animal mortality policy for your clients.
==============================================================================For the policy in question, try to find a section labeled similarly to “Property Not Covered” or something similar. For example, the ISO HO 00 03 05 11 form under its “Property Not Covered” section excludes animals, birds, or fish.
Are you asking about first party coverage? Or third party liability coverage? There is probably no property coverage for the death of a homeowner’s pet, but I can imagine some circumstances in which liability coverage for the injury or death of an unrelated party’s pet might be found.
Liability coverage for pets injuring others is covered and is one of the largest causes of personal liability claims. Many auto policies are adding a pet injury benefit to cover pets hurt in auto accidents. Pet medical plans have become widely available, but I've not seen animal mortality for animals smaller than livestock.