Firstly I headed over to Frayfeather Highlands in Feralas, which is fortunately easy accessible to a druid via the Emerald Dreamway (though trying to find it on the map was a bit of a bother - I had to ask McTacky for directions) and all I had to do was find an egg and stand on it and read the little emotes in text.
Oh? Is this egg moving?
The egg seems cold. Stay close to it to keep it warm.
You hear a rustling sound inside the egg.
The hippogryph inside is struggling to escape.
This is it! The egg is hatching!
It only takes one minute and then we have a hippogryph hatchling sitting on our shoulder like Pepe on our head. So if you love Pepe, you will love this once a year hippogryph hatchling.
It made my shoulder and head armour disappear! And on my druid it appeared in different spots on me.
It also made tweeting sounds and various emotes for the rest of the night when I was dungeoning. I thought it was specific to what I was doing (dungeons, WQ, PvP) but it appears it was just random!
Your Frayfeather Hatchling sighs contentedly.
Your Frayfeather Hatchling seems to be learning.
Your Frayfeather Hatchling starts to doze off.
Your Frayfeather Hatchling wants to see more of the world.
Your Frayfeather Hatchling seems bored.
Your Frayfeather Hatchling seems impressed.