The first quest I discovered, and the one that I've seen the most so far, is called "Shrimpin' Ain't Easy". It requires you to fly to Zangarmarsh and fish up a few Bloated Barbed Gill Trout. You can catch these by fishing in any of the lakes in the zone. Once you reel one in, you can open it like any other package in the game to collect a few shrimp and gray items. One fish can hold multiple shrimp and this quest can be completed pretty quickly, assuming that you don't encounter any bugs. Currently, I often encounter a bug where I'm unable to catch any fish (aside from the special fishing pools, which don't yield the quest fish) in Zangarmarsh while on this quest. Abandoning and retaking it has fixed the problem every time so far.
"Bait Bandits" is the next quest I found. It requires you to fish up the elusive Blackfin Darter in any of Terokkar Forest's rivers. For this quest you only need to catch one of the quest items, so as you might expect, it has a relatively low drop rate. While the quest text can be a little confusing since it seems to give you special instructions on how to catch this fish, you don't need to do anything special. Old Man Barlo's instructions merely seem to be there to add flavor to the quest, and you don't really need to "pull your line at the last possible second", at least as far as I could tell.
The third quest, "The One That Got Away", takes us to Nagrand. This one is similar to the Terokkar quest in that you only have to catch one unique fish. In this case, you need to throw your line in one of the zone's lakes until you are able to land the World's Largest Mudfish. While I got him on my fifth cast, others in the zone were complaining about the drop rate.
Two more quests are currently appearing on Wowhead, although I have not seen them on either of the US PTRs, so I can't provide any more information than what is currently listed on that site. "Felblood Fillet" will apparently take us to Shadowmoon Valley or Hellfire Peninsula in search of a Monstrous Felblood Snapper. The other quest, "Crockolisks in the City" will send us to either Orgrimmar or Stormwind to catch a Baby Crockolisk.
In reward for your daily efforts on these quests, you're given a Bag of Fishing Treasures. This little cache always contains some gold in addition to various other rewards. Personally, I've only found gray items (that sell for a couple gold) and Sharpened Fish Hooks, that act exactly like Aquadynamic Fish Attractors. Other players have reported a green-quality cooking recipe to make Captain Rumsey's Lager, that makes you slightly tipsy and increases your fishing skill by 10 for 3 minutes, and the blue-quality Weather-Beaten Fishing Hat, that has +94 stamina and functions as a reusable +75 fishing lure.
In addtion to these quests, there are reports of new fish being found on the Isle of Quel'danas (a.k.a. Sunwell Isle). The Bloated Giant Sunfish is said to contain random BoE green-quality items and the Luminous Bluetail acts as a sort of mana potion. As is to be expected, the latter shares a cooldown with mana gems and other such consumables.
I'm looking forward to all these changes hitting the live servers, and maybe even discovering more as time passes. Are you an avid fisherman? Are you looking forward to these changes as well?