Fantasy has a few different definitions depending on how you define it. It can be applied to any work that's make-believe, though most usually use it to define the sword and sorcery aspect in the vein of Lord of the Rings, Dungeons & Dragons, and the like. The kind that usually focus on a more Western approach with knights, kings, castles, magic, which Avatar doesn't. The "magic" in Avatar is fairly limiting, as opposed to say Evil Lyn in He-Man or Phobos/Nerissa in W.I.T.C.H., and depending who you talk to, magic is an important aspect of fantasy.
It can be classified as Asian Fantasy, I suppose, like samurais, ninjas, martial arts, stuff shows like Inuyasha or Dragonball focus on, but it's definately not in the same vein as the other two thematically. It's a bit more.. limiting than fantasy usually is, I guess I'd put it that way. The only "magic" is one of the four elements (technically three, since Aang is the only Airbender anymore) or they use a weapon of some kind. Where as traditional fantasy tends to lend to more creative uses of magic and creatures.
I haven't personally seen World of Quest, though it seems more of a comedy/slapstick action show (like Ying Yang Yo or El Tigre are) with a focus on fantasy than a serious action show. I've never even heard of Jane and the Dragon, and I thought Magi-Nation was a card-game show.