From WoWWiki

Fishing Pole refers to the basic starting fishing pole with no fishing skill requirement nor level requirement to equip, and no bonus to fishing skill. You can purchase it, wield it, and use it as a melee weapon with no fishing training, but you cannot fish with it until you are a train in Apprentice Fishing.

All characters will begin fishing using this item. (You may have access to  [14] The Family and the Fishing Pole quest that awards the [Blump Family Fishing Pole] with only beginning level fishing skill requirement, but that quest requires you to fish for six Darkshore Groupers - either with a basic Fishing Pole, or with a pole you were able to obtain after you trained up your fishing skill with a basic Fishing Pole.)

Source

The Fishing Pole is sold by trades supplies vendors and fishing supplies vendors, and is widely available. All the fishing suppliers will have them in stock.

Notes

For the Alliance, the Fishing Pole is available for free from a couple of sources. The quest  [6] Red Snapper - Very Tasty! is offered by a fishing vendor on the road from the Draenei beginning area to Azuremyst Isle. For the above mentioned The Family and the Fishing Pole quest, Gubber Blump will lend you a Fishing Pole if you need one, and nothing prevents you from walking off and using it elsewhere.

The Fishing Pole is very cost effective. If you have a decent income you might want to trade up to the [Strong Fishing Pole] for +5 fishing skill; but consider that the Fishing Pole is disposable and replaceable when your bags get full, and you can buy 20 [Shiny Bauble] lures for the same money as the Strong Fishing Pole. They grant +25 fishing skill lasting 10 minutes each, 200 minutes total for twenty of them, that's a lot of fishing time, plus you don't have to spend it all at once, just buy the lures as you need them. +5 fishing skill will not help much at low levels, but just one Shiny Bauble when you first start fishing in your starting zone will allow you to quickly pass the no missed catches level 30 fishing skill - or just one [Bright Baubles] in your capital city to pass the no missed catches level 75 fishing skill for the slightly harder fishing areas. In the hardest areas +5 is not nearly enough, and you are going to want a much better fishing pole anyway. (Although, at fishing skill level 375, the Fishing Pole and a +100 fishing lure will give you 475 fishing skill. This is enough to fish in all fishing locations and to not have fish get away in all but the hardest areas.)

External links

Fishing Poles
Fishing Pole • Blump Family Fishing Pole • Strong Fishing Pole • Big Iron Fishing Pole Seth's Graphite Fishing Pole • Nat Pagle's Extreme Angler FC-5000 • Arcanite Fishing Pole