Olly

Olly is my new friend, as of today.

To unlock the ability to buy the other faction's pets from him, you first need to complete a mission at your mission board. This mission is tied to a quest which is started from A Shady Message. This item starts the quest. I obtained this item randomly after I won a PVP pet battle through the find battle queue. I don't know whether you can receive it through other pet-related means, but that's how I got mine.

So at this stage, I'd recommend winning PVP pet battles to try and get access to Olly, the Pet Smuggler.

He warns that his pets are difficult to obtain and will not come cheap, but you need not worry. The prices are the same as the alliance vendors' are.

He sells:

Greatwing Macaw - 50 Polished Pet Charms

Drustvar Piglet - 75 Polished Pet Charms

Mechanical Prairie Dog - 75 Polished Pet Charms

Abyssal Eel - 75 Polished Pet Charms

Bilefang Skitterer - 100 Polished Pet Charms

Frenzied Cottontail - 300 Polished Pet Charms

Sadly, at the time of writing he is not offering pets requiring Alliance-only reputations, such as the Seabreeze Bumblebee. He also does not sell Bumbles, which is part of a long quest chain, similar to the Horde's chain for Kua'fon.

This vendor is to sell the items that were previously Alliance only pets in 8.0. To find this vendor you will want to go to 45.51, 86.45 on a set of stairways in Dazar'alor. For those who don't have coordinates, the best way to explain this is go where you would queue up for Island Expeditions or the Motherlode dungeon portal. Close by is a set of stairs, you'll want to take this stairs and go up past the first floor and then take the next set of stairs (so _/¯) and at the top of that stairs off to the left you will see a bunch of crates and baskets piled up. On one of the baskets is a little orc kid, named Olly.

You will need to do the mission [mission=2122] for the actual vendor to show up, otherwise you'll see [npc=123169] standing there. The vendor will require you to win PvP Pet Battles (hooray /s) in order to get the message to spawn. Do note that it could take you 1, 10, 100, or even 1000 PvP Pet Battle wins just for it to show up and isn't guaranteed. If you play only one faction then this might be the only way you can get these pets (I am not 100% sure if they are cageable). If you level a toon on the Alliance side you might be better off just unlocking them normally since you might want the paragon pets anyway. It's also been noted that some of the pets can be unlocked by a vendor in Drustvar as well, making the Horde shady vendor a bit less useful as the Alliance counterpart, Dodger

Once you do unlock the vendor you'll be allowed to purchase the following items.

[item=163489]
[item=163493] *Note can be obtained by unlocking [npc=142197] in Drustvar
[item=163492] *Note can be obtained by unlocking [npc=142197] in Drustvar
[item=163495]
[item=163496]
[item=163494] *Note can be obtained by unlocking [npc=142197] in Drustvar

Olly is sitting on a basket at 45.5, 86.5 in Dazar'alor, or 56.5, 57.9 on the greater Zuldazar map. There's a Skullsplitter Thug standing next to him who doesn't have anything to say, and Olly had nothing in his vendor window when I visited.