Four new fishable pets are coming in patch 5.2, and El from El's Extreme Anglin' has a guide on how to fish up all four!
It seems as though the catch rate is approximately 1 in 5,000 but casting into pools of fish may be significantly more efficient than open water fishing. Either way, it'll be a challenge to fish up all of them. With the droprate of the Nat Pagle fish being increased, though, I'm sure we won't come away completely empty-handed. :P
Although each fish is supposedly "unique" (to a zone), El has provided strong evidence that that may not be the case. One Emperor Salmon School should not differ from another Emperor Salmon School, even if they spawn in different zones. This will be something that needs even further testing to confirm, though. I bet El's just the right angler to do it too. ;)
I'm definitely bookmarking El's guide for future reference; it will come in handy in the upcoming patch.
PS: So glad I managed to get the Ancient Pandaren Fishing Charm recently. Hopefully this little doodad will increase my chances to fish up the Tiny Carp pets! XD