Seems like the ancient Egyptians worshipped their pets just as well.
This is not the case to leave a huge estate to the pet — but it is only prudent to separate out some funds specifically for the care of the pet and name someone, with whom you made prior arrangement, to take care of them, as well as include something additional for the trouble. Otherwise even relatives or people you think you can trust and leave them your estate may just dump your dear beloved pet at a shelter, where it may well be euthanized.
In many cases pets are more deserving than people — they never criticize, they just love you unconditionally — it’s only reasonable to make sure they are taken care of, after you are gone and not leave it to chance or someone’s whim.