For the Horde Hunter wishing to be unique, there are several pets you won't find in Horde areas until later levels, and acquiring one of them will certainly make you stand out.
Owl: There are low-level owls in Teldrassil, the Night Elf starting area, but you won't see any other owls in the game until you hit Felwood in the high 40s. For the ubiquitous Night Elf Hunter, an owl isn't an unusual pet -- but for a Horde hunter they're much less common. Why? Because to reach Teldrassil, you have to run through the Night Elf city of Auberdine to catch a boat to the Night Elf capitol of Darnassus. Teldrassil is only accessible by running through Darnassus. Ouch! But if you go to all that trouble, the prize is a cool-looking pet that all of your friends back in the Barrens are sure to envy.
Ravager: You may think that Ravagers don't appear in the game until you hit Outland -- but you'd be wrong. There are two different varieties of Ravager on Bloodmyst Isle, the Dranei starting area -- an orange one (level 9 - 10) and a green one (level 16 -17). Getting here isn't quite as bad as getting to Teldrassil -- at least you don't have to run through an Alliance capitol city -- but it is pretty bad. You have to run through Auberdine and catch a boat to Bloodmyst Isle, just like you were getting an Owl, except after that point you don't have to run through any major cities. But for a Horde character, it's still a long and dangerous trip. But in the end, you'll net a pet no one else will have until Outland!
Spider: Not just any spider, of course! But there's a menacing-looking spider named Zarakh with a unique model out on Bloodmyst Isle that you might like. There's also similar, but differently colored spiders called Myst Leechers out there. Sure, you can find similar-looking spiders, but not until you get to Outland.
Bear: There are few bears in general in the low-level Horde areas, but a couple out in the Alliance zones have such a unique look that they can't be ignored. Want a white bear? There's one in Dun Morogh, the Dwarf and Gnome starting areas. No major cities to run through, but you'll pass plenty of guards getting there. The next white bears start showing up in Winterspring in the low 50s. Or perhaps you don't want such a clean-looking pet -- there's a torn-up looking bear on Bloodmyst Isle, similar to those you'll see in Felwood in the upper 40s.
Tallstrider: I'm not sure why anyone would really want a Tallstrider. From a practical standpoint, they have no interesting skills. However, there are a few out there with very interesting skins. In the Alliance zone of Darkshore, you can find a brightly-colored Strider Clutchmother, but she's a rare spawn and won't always be around. And closer to home, in Mulgore, you can find Mazzranache, a bright pink Tallstrider. (But since Mazzranache spawns so close to home for many Horde players, you may not find it completely rare.)
Cat: Since, when I first started my hunter, I asked you all what pet I should tame and you advised a Cat, I've decided to stick with that by picking up the transparent Ghost Saber from Darkshore. (Remember them? Mike wrote about them recently.) While it was a long run to fetch it, running through Ashenvale and Darkshore, all I had to do was stay on the road and I didn't run into any Alliance guards or other major trouble. And now, I have a pet that I've yet to see the like of in any of my Horde-side leveling. And the perfect name for a Cat that's never entirely there and never entirely gone? I call mine Schrodinger.