WarcraftPets isn't sure if you have to log in tomorrow (Sunday the 23rd) to get it or if it'll just be mailed to everyone tomorrow -- I believe you can only get the Achievement for logging in on the day itself, but the pet is a little more confusing.
The pet is Bind on Account, so if you don't feel like logging on to ALL of your characters, you can log on to one per server/faction and just mail the pet around to everyone. Also, it's a good idea to keep it on at least one of them (I tucked it away on my bank) so you can send it to all your NEW characters to train later on.
Just make sure to log in sometime on Sunday the 23rd to secure this snazzy achievement and pet. You get it just for existing, so. ^_^
[Edit]: It's Monday afternoon. I logged in on an alt and got both the Achievement and pet. :) So if you didn't log in yesterday, you can still get them.