WoWDB

Fun story: Alayea and I did this achievement by opening eggs in Bloodhoof Village, Mulgore, until we both had the bunny buff with roughly the same duration. We proceeded to run all the way from Bloodhoof to Golakka Springs, Un'Goro Crater via Thousand Needles and Tanaris. It took us approximately 50 minutes to travel there and we alternated who led and who /follow-ed. We didn't realize that the intended means of earning the achievement was to grab a partner and use  Blossoming Branch...

Despite being what most people would consider time wasted, it was fun. Especially when we crossed from Thousand Needles (now underwater post-4.0.1) into Tanaris through that narrow passage in Shimmering Flats - there was this undead player on a mechano-hog that rode past us, stopped, then backed-up and turned around to look at the hopping bunnies. I would have paid to have seen his or her face in real life. XD

Unfortunately, it wasn't possible to carry on the tradition since Cataclysm put a big ol' gate between Mulgore and The Barrens. We haven't tried it from Razor Hill in Durotar because it's a much longer distance and, well, it just wouldn't be the same. :(

More on topic: It is possible since Cataclysm to solo this achievement by setting your hearthstone to Marshal's Stand and traveling to one of the villages participating in Noblegarden. Open the eggs until you are turned into a bunny. Hearth and hop your way to Golakka Springs. Sit - can't lay an egg if you're swimming - and wait until the egg is laid. Congrats on the achievement.

Bring some friends and some Blossoming Branchs to Un'goro crater during the Noblegarden holiday and turn each other into rabbits.  Then just sit around until you, well, lay eggs.