(Whoops, wall o' text! I tried to divide it, anyway.)
It could work and would make animals seem less static. In particular, I think breeding needs to be redone. Some kind of mating season could be added to creatures through the raws (if they have one); when it's the right time of year females could periodically attempt to find a mate by assessing the distance of any uncaged males (if they are any), starting with the nearest ones and doing the farthest ones last and having the males attempt to calculate a path to the female. You can think of this as "pheromones," if you want. The distance check is important - ideally males should not have to calculate a long path to a female, which could lower framerate. If a male can successfully path to the female, it will move to the female's position, stand on it's tile for a short moment, impregnate the female, and then do whatever after that. If the male can't path to the female the female can flag it as "checked" by that female and have a farther male attempt to path to it, until it eventually finds a mate, if it still hasn't found a mate after checking all the males it could retry 7-14 days later. If there aren't any unimpregnated, uncaged females or there aren't any uncaged males, or the mating season ends the pathing would cease altogether. It's unobtrusive enough you probably won't notice it and hopefully wouldn't eat up too much cpu, but would require actual contact between the animals.
The role of water is downplayed in DF and I wonder how pets would survive in a booze-only fort. Besides, you know, getting boozed up. But since Toady has promised much more underground features in the next version water could be more plentiful in dry areas. Tamed animals should require water to survive like your dwarves and could periodically path to your designated water source (unless it's completely covered by a well...) and drink from there. Simple. Requiring wild animals to drink might not be necessary, we can assume they're getting water somewhere on dry maps, but it could be interesting to have them gather around water sources far away from your dwarves and pretend to drink. If you're keeping your animals in pens you could build a trough, which would function to hold several units of water for the animals to drink (abstracted, though you certainly could dig a channel and have an actual pool) and your dwarves could periodically refill it if it got low. If the animals are caged dwarves could fill up a bucket and stuff it in the cage for any animals inside to drink, otherwise it would work much the same. Could possibly have a dish item specifically for this that could be built out of rock.
Food would work pretty much the same way as water, but there'd be a few extra things. For one, carnivores should eat meat and herbivores should eat plant matter. You know all those elephant organs a few people were getting grossed out about in the screenshot toady posted in the dev log? The inedible (to dwarves, anyway, though I'm not sure what they consider appetizing) bits could be turned into a sort of mash not unlike wet dog food and fed to any carnivores. I'm not sure if large carnivores (lions, for example) should eat mash, but whatever. They could also eat plain old meat if there wasn't any mash though. Large herbivores could be fed hay gathered outside, or could be fed straw made from threshing cave wheat or longland grass. Smaller herbivores (certain rodents in particular, a guinea pig is a familiar example) could likewise be fed hay as well, but could also be sustained with fruit. Like with water, there could be troughs or dishes to serve the purpose of feeding, though dwarves could just as easily throw food on the ground for dogs or hand-feed vermin.
EDIT: It just occurred to me that a gestation period in the raws would be very appropriate, and females could pass a simple check before attracting males to simulate how actively the creature mates, or simulate the pregnancy rate.