There's a pretty strong argument now that domestication doesn't have to involve active selection by humans. Eg dogs: there wasn't some early human decided it would be a good idea to confine wolves, test them for temperament and select the nicest ones to breed from. Instead what probably happened is that some wolves started exploiting garbage dumps and latrines as food sources. Those that had shorter flight distances (and therefore could tolerate humans being a bit closer) got scared off less often and so ate more and so were selected for. The food was plentiful and easy to get, but not great quality, so there was also selection towards smaller brains (since they are expensive to run, and dogs needed them less). Smaller heads and brains being one of the things that distinguish dogs from wolves. The result was 'village dogs' similar to the often-assumed-to-be 'strays' found around human settlements worldwide today living on garbage. Arguably you don't get active selection till a long way down the line. (For more read Coppinger and Coppinger 'Dogs: A new understanding of canine origin, behavior and evolution')
The domestic cat also probably just moved in, and their breeding has only been widely controlled very recently. However 'domestic' cats that are not socialized with humans during a crucial few weeks as kittens are feral, scared of humans, capable of inflicting quite severe damage on them, and nearly impossible to tame. Are they really domestic then?
I've heard it said as well that horses were in many ways 'pre-adapted' in ways that made them easy to domesticate.
You could say that about bearded dragons. I hear they make great pets (in fact there's a pet one living upstairs from me, which I've stroked when it's out riding on it's owners shoulder). You can get them, custom made viv set ups for them, pelleted food and live food from Pets at Home.
All in all I don't think you can say that there's a catagory of 'domestic animals' that were created by humans, and are in some way totally different to all 'none-domestic' animals. The reality is surely more complex than that?
It is an interesting question. To be honest I have thought that if I was starting up a zoo I might include some 'pets' to start. Pets at Home New Malden usually has quite a range including dart frogs, horned frogs, water dragons and marine fish (including 4 kinds of scorpion fish on one visit). I think stuff like that can make great exhibits depending on how they are exhibited.
Interesting about the meercats: it would indeed be intersting if zoo animals started to change with the change in their enviroment. Some (like Copinger and Copinger *G*) would probably argue it would be inevitable.