The health and safety code of your state as well as federal laws may prohibit the consumption of certain animals.
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I agree with Mr Patrick that there are likely federal and state laws to prohibit you from eating your cat, goldfish, hamster, dog, gerbil, parakeet, whathaveyou... But there are certainly ethical and moral issues involved with eating your "pet" or as I prefer to say, your "companion animal" versus a non-domesticated non-companion animal. Many vegan or vegetarian humans are against the consumption of other sentient creatures because they can feel pain and are aware that they are suffering on the way to your table. It is not a pleasant path.
Other humans feel that we are the top of the food chain, so what the hell. Bon appetit! However, we do not have the largest brains, we are not the only creature to communicate, love or mate for life, yet we are the only animal that systematically destroys itself, its habitat, and every other creature and its habitat in the name of our own progress. Now THAT'S something to be proud of!
Can you eat your dog? Not likely. Should you eat your dog? Even less so. It's about as smart as eating your own foot.
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Most states do not allow the killing of "domestic" animals except by a veterinarian or under extreme circumstances (such as a dog attacking livestock) and to do so is animal abuse. In addition, most cities/towns/municipalities/counties/etc have laws regarding the butchering of animals by private citizens (i.e., non-butchers), with possible exceptions for game animals such as deer.
Kentucky cruelty to animal laws are somewhat vague as to what you propose, though, arguably, they would forbid it. You may wish to speak to a local animal law attorney before proceeding.
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