Wowhead has a great guide on the new Darkspear Rebellion (coming in 5.3), how to access it, and how to complete the quests/dailies/collect things in order to purchase the vanity items. Why should you care? It's how we'll obtain Gahz'rooki!
As their guide details, you'll need to complete two scenarios before heading to Kalimdor to aid your faction in the rebellion. And yes, both factions will be able to participate and purchase the pet.
Keep in mind that although these events will mainly occur in low-level areas, the quests and mobs associated with them will be level 90. This means that only maxed level capped players will be able to participate. Lower level players will likely need to purchase Gahz'rooki from the AH or trade with another player. Although the pet is BoP, it can be caged.
To purchase the pet from the Darkspear Rebellion Quartermaster, you'll need to earn one Radical Mojo. The only way to earn this item is by completing a weekly quest called Battlefield: Barrens (available to both horde and alliance, with the same objectives).
Before unlocking the weekly, though, you'll need to complete the quest chain first. During the initial chain, you'll complete the quest which will ultimately be the daily necessary to earn a Radical Mojo. You can preview the quest line on Wowhead's guide.
It's going to be an interesting experience, especially for PVP servers, joining both factions in one area and "working together". We'll see just how much coordination and cooperation there is between players, heh.
I can't wait to get Gahz'rooki, as I've always wanted a baby hydra! I'm quite pleased that the path to obtaining this pet isn't too long-winded, and should anyone not want to participate, they have the option of trading or purchasing it elsewhere. Yay for options. :)