There are two methods of accomplishing this achievement:
The easy method is to group up with another player who also possesses a and trek down to Golakka Hot Springs as a party. Use the branch on each other and then wait for an egg to pop.
The hard way is to get transformed into a rabbit randomly by looting Brightly Colored Eggs, hearth to Dalaran and then take the port to the Caverns of Time in Tanaris (or hearth to Cenarion Hold in Silithus), then hop all the way across Tanaris and Un'goro Crater. Taking damage of any sort (fall damage, combat) will break the costume, so be careful. Once there wait for an egg to pop.
Patches and hotfixes
Patch 3.1.0 (14-Apr-2009): Added