Unfortunately, it seems that co-op won't be online, as only SpotPass and StreetPass have been mentioned. This is a shame, since the multiplayer is described as "extensive" and Square Enix plans to create a whole community based around the game.
StreetPass and SpotPass will also be used to acquire all sorts of powerful items and weapons, with 3DS systems trading gear automatically and Wi-Fi hotspots dishing out rarities and new challenges. Dynamic dungeons are a big part of the game too, making this a game with potential to last quite a while.
The game's being shown off at E3, so I may have to sneak over there and give it a try.