I've moved them from time to time...
When I first started collecting, the numbers were small enough that the bank's pet care service was enough...then the mages came up with this neat trick to allow me to summon them from anywhere, so the first move began. Outland was out of the question...I'd never forgive myself if one of them fell off the edge while I was away.
I briefly considered Orgrimmar, but decided against it because I didn't want them to feel fenced in with all those walls, and Thunder Bluff had the same concern as Outland. Silvermoon and its parks would've been ideal, but those stuck up elves wouldn't let me keep them there. Undercity didn't get enough light, either.
Ultimately, I found areas they liked and moved them there for periods of time, but found nowhere parmanent until my people's ancenstral homeland of Pandaria revealed itself. After speaking with the celestials, the agreed a home needed to be found and as such they crafted a small island shrounded in the remaining mists, one that had diverse places for them to play and keep all of them happy. I think the fact that I adopted their children had some say in the matter, but no matter the reason, all my little friends have a place to live happily when I haven't called them to my side