There is a spectrum of opinion [wikipedia.org] on what "animal rights" means. At the very least, I think animal rights include the right not to suffer needlessly at the hand of humans. I doubt anyone would argue that is also a human right. So, continuing in that direction, I don't think it's a stretch to imagine that many human rights can be accorded to animals also.
More tangibly, this reluctance to abuse other species with certain characteristics is what lead to the domestication of cooperatively useful species (dogs, cats, cattle, etc). But our moral compulsion should not be mistaken for some sort of universally true innate "right".
It seems like these questions are at the forefront more and more these days: what is a right, where do they come from, and how do we know? And your comment touches on another very important point relevant to this thread: animals do have jobs, we just don't pay them a salary beyond food and care. Think of animals in agriculture and transportation, hunters' assistants, seeing-eye dogs and other service animals. Heck, they're even actors. Animals can be said to have jobs in the same way humans do, and in fact we've been working hand-in-paw with them for as long as we can remember.
I know some animal-rights organizations love to call these types of animals "slaves" but there's clearly something different between humans and animals. It just becomes very difficult to pin it down as something other than a matter of degree when we don't even clearly understand the nature of our own consciousness.
Personally, I don't believe animals have rights - I do however believe that we have responsibilities toward the animals, and are under moral obligation not to cause undue suffering. Experimenting on animals is therefore ethically a very sticky area.
BTW, there's a very good graphic novel about Laika that's historically accurate, based on information that became declassified after the fall of the Soviet Union. It's targeted toward adolescents, but worth a read.