I've never heard of any company offering bereavement leave for the death of a pet, and the idea has never crossed my mind.
I think it's a nice idea and would support it of course, but I suspect the length of time for leave would be shorter than for the death of a human family member. The main logic being, if, say, a spouse dies, you now hold all of their responsibilities on your shoulders (e.g. income, chores, childcare, etc), whereas with a pet dying, you probably have fewer responsibilities excluding any financial or end-of-life duties. Obviously, the emotional toll can be just as significant for a pet as for a human, though, which is why I'd still support pet bereavement leave.
Edit: for people worried about employees exploiting it by having a bunch of hamsters or fish or something, just limit it to something like 3 days a year. It sucks for people with tons of pets, but I assume getting 3 days off a year would cover most people pretty well as I doubt the average person has more than one pet death per year (thinking in terms of cats and dogs here).