I do. And I love it.
Currently doing it on my third hunter. As soon as I could tame and was the right level I went for the Skitterweb Matriarch (need I say it, LOVE her skin. Amazing pet in pvp.). Around the same area but a bit higher level I got Ressan the Needler, and yesterday I went for one of the red spiked raptors in Echo isles. Btw, I'm a draenei so you can imagine the travel

So do you guys do it? Just for the thrill of having something different around? Cuz I love having a spiked raptor with me in bgs while all the rest have the brown Redridge fox. Teehee!