Onyxian Whelpling was mailed to any players who logged on during WoW's 5th anniversary celebration back in 2009. As it isn't cageable and wasn't acquired by redeeming a code, this is one that seems to be truly classified as "Unavailable" if you weren't playing 6 years ago. I've never heard of anyone getting it through the BMAH, but then with Blizz you never know.
Baby Blizzard Bear (2008 anniversary) and Molten Corgi (2014 anniversary) fall into same category.
Another unavailable Dragonkin is the Spirit of Competition. It was an occasional drop from winning a battleground during the 2008 Beijing Olympics, it's modeled after the classic Chinese dragon.
Any pets that you get by redeeming a code are still possible but as Buruan pointed out, can be expensive. Not entirely surprising as it means someone had the foresight to save a code and not use it in hopes of selling it years later. Murky (Blizzcon 2005 pet), for example, is on EBay today for "only" $3,950.00. Well you do get free shipping
There's some hope with the pets that were originally only available on overseas servers. Four of the China promotional pets have been resurrected through Recruit-A-Friend. If you can't sucker a friend into signing up, works out to only cost around $40 each to recruit yourself to get the pet.