You should buy some lures if you want to fish in the Oases. Anywhere you can successfully catch fish will give you skillups, including in a "lowbie" zone like the racial starting areas (Teldrassil, Dun Murogh, Elwynn Forest, Durotar, Mulgore, and Tirisfal Glade) or a major city. If you wanted, you could fish from 1-300 in the waters of a capital city (excluding the quest to gain Artisan fishing).
Please check out the Trade Skills Sticky thread -- there is some information on fishing beyond what I provided and will probably answer questions you haven't thought to ask yet.