This Gamespot.com article includes references to the racial mounts for the two new Burning Crusade classes.
Like with all other standard mounts in the game, both the elekk and cockatrice will, as Chilton puts it, "look cool and go fast," though they won't possess any exceptional powers.
Information is Growing
Little is known about them at this time, and in fact this picture is not confirmed as the Elekk (although it is suspected). The links below are "under construction."
The Draenei Mount: The War Elephant
The Blood Elf Mount: The Mythical Cockatrice
Also keep watching The Burning Crusade Bestiary for more information as well.