Just confirmed on the 4.3 PTR that if you log out on the Darkmoon Island prior to the faire ending, you'll get teleported back to where you zoned into the island once you log back in after the faire ends. Boo. That means you can't access the island if the faire's not in town.
Looks like pet collectors will only have one week out of each month to farm for the Sea Pony. It shouldn't be too bad since the drop rate doesn't seem nearly as bad as say... the Fox Kit. Not to mention you can fish in relatively safe zones without fear of being ganked over and over, and there's really no threat of people "stealing" your kills.
Whether or not the limited farm time will make this pet more rare, I don't know yet. We'll have to wait and see what actual droprates are like once patch 4.3 is released (coming soon! yay).