First of all, I should point out that I do not believe in natural rights. Nature does not grant you any rights. In fact , if you are thrown out in the middle of nature you are likely to starve or be eaten by a wild animal if you do not use your intelligence. Nonetheless, societies do develop certain legally enforceable rights. These rights are, essentially, claims that may be backed up with force. They may be based on any number of reasons, both good and bad. As a libertarian, I hope that the legal rights of a society are individual rights as I believe that that regime of rights results in the most satisfactory state of affairs for both individuals and society in general.
Re: Animal rights. My opinion is that animals should be granted limited rights depending on their level of intelligence and their ability to suffer and feel pain. I don't think ownership of any animal should give you the right to torture it for your pleasure. There was a man in this area who tortured and killed cats by twisting their necks and throwing them against walls. This behavior really made me sick and I have a hard time imagining a good defense for it. (I have two kitties and I love them dearly.) Any society that would allow this behavior on the basis that "animals are property and therefore you may do with your property what you will" is not one that I care to be a part of. Unlike cars or pens, cats are sentient beings and that ought to limit what you are allowed to do with them.