Well, it's a re-work of the Monk - but it's not too much more.
The base levels 1-2 would be fine - but it's around level 3 where the re-writing would need to start.
Levels 1-2 is equivalent to the training a bender gets, cause all of style of bending involves a significant amount of martial arts - though they may not actually use their hands and fists to the same degree that a traditional DnD monk does. All of them can throw a punch - it's mostly bending that actually does most of the damage.
Level 3 and forward is where it'll get messy.
The Monk is assumed to be a frontline fighter, benders are not - they are indeed both back and front line dependent on the individuals style. They have a variety of blasts and area control. In that way, they're closer to the 4e Wizard. There is another hang up also, is that DnD likes to specifically spell out spell effects - "spell a does x", versus the more malleable style that benders are portrayed as using - they control the size, power, shape, and intensity of their bending effects. So even something as simple as a fire blast can be different every time because of the intention of the strike - it's less hot, more hot, goes further, is point blank, etc. Should you make a spell for each possible iteration of the fire blast? Or the ability to lift a boulder, or multiple boulders, or one giant boulder?
I think they should learn "spells" that can be malleable via Ki Points, but they would be very very open ended in a way - they learn the Elemental Blast ability at level 3, which is the most basic offensive use of bending and a few non-offensive uses like Elemental Attunement. Then, at 4th one new ability, and every 2 levels after. They can drop things like slow fall, stunning strike, and a few other class aspects that don't actually jive with benders, and are more akin to gurus.
Each sub-class would actually be an element, and the sub elements would either be built in options of that sub-class like metalbenders are earthbenders who chose to take those abilities instead of the more general earthbender abilities.
I mean there is a whole laundry list of changes and homebrew if you want something I think that could emulate the show and the universe much more truthfully or accurately. In a way, you'd have to re-write the basic premises of DnD (general premise; as the DMG encourages you to do this), but a game with benders would be a game where they're only things close to mages, and there are no warlocks, clerics, wizards, or anything like that. If you wanted to play a more general DnD world, with benders re-flavoring warlocks would work or just using the monk.
There's a lot of ways to tackling this, from making a singular class to making maybe 4 distinct classes - especially if you're going the route where benders are the only "magical" people around. Firebenders would be more offensively inclined, less area control, and probably closest to fighter in terms of capabilities. Earthbenders would be defensively oriented, less movement, love giant attacks, and definitely love area control. Waterbenders would be the closest to your clerics, but excel at control of opponents and can do pretty good area control. Airbenders - if they weren't pacifists - make the best ninjas and have the best movement, stealth, and some area control.
These are just some thoughts I have about the world in terms of game design - but you definitely have to evaluate from the ground up, and plopping benders into a world that doesn't support them is going to cause a little chaos. Cause they're a little of monk, wizard, and warlock all rolled into one.
