The Pandaren race will be available in the next patch, and you don't even have to get Mists of Pandaria to get them.

Blizzard announced on their blog that with the upcoming Patch 5.0.4, the new Pandaren race will be available to all players without the need of the upcoming expansion pack. 

The blog states:

"With the release of patch 5.0.4, we're making all the races of Azeroth playable by anyone, no matter which version or expansion of World of Warcraft they own. This includes the enigmatic pandaren, who will become available for play when Mists of Pandaria is released on Tuesday, September 25. We want the entire World of Warcraft community to be able to embrace their inner goblin, blood elf, worgen, draenei, or pandaren from the moment they step foot into the world of Azeroth."

World of Warcraft: Mists of Pandaren will be available September 25th.