Short answer - yes.
You want to get to a scale and weigh your truck and subtract that from the GVWR to get your actual payload capacity. Should be your next step before doing anything else. Actual payload weights are always less than the advertised payload number or what's on the door jamb sticker. If your truck has any add-ons or options, that comes off the 1600 number right off the top before you even look at available payload cap.
Throw any dry weight numbers on the trailer out the window. They're useless for anything. Actual trailer wt. and tongue wt. will be MUCH higher. You could easily find your truck is overloaded on payload and then you'll be sorry, unless you want to drive way overloaded. The capacity of 2240 I assume is cargo carrying capacity? That is BS.
I like to give our recent experience with a brand new TT as an example. Dry wt. 5237 lbs. Actual = 6600 lbs. GVWR is 6800 lbs. Dry tongue wt. 518 lbs. Actual = 960 lbs. Cargo carrying capacity (NCC) 1563 lbs. Actual cargo capacity left after adding basic cargo = 200 lbs. Axle ratings are 2 x 3500 lbs and max. total tire capacity is 7280 lbs. Our trailer is designed and built almost to the max. available capacities and leaves very little left over for either a safety margin or additional cargo capacity. None of the factory options/upgrades are included in the UVW which drives the actual weight up drastically. This is common, so check everything out very carefully, and don't go by the fairy tale factory dry and payload figures. I can't believe that we can't tow with even a full tank of fresh water without being overloaded.
Then there's the issue of frame strength on a trailer of that length and weight. If it's got a Lippert frame that has I-beams made from welded together 1/8" sheet steel, look out. Happy to elaborate if wanted...
I'm guessing the tongue wt. of your proposed trailer is up in the neighborhood of 1200 lbs and the actual wet/loaded trailer wt. will be something like 7500 lbs. I'm willing to bet big $$ that your truck ain't gonna have the payload capacity. Plus you are approaching the max. tow capacity and are going to find yourself under-powered at times. Keep in mind with your available actual payload capacity, you have to be able to add the DW, kids, in-laws, groceries, tools, and other "crap". You will probably not have enough payload for even the driver + full tank of gas with that trailer. There's also GAWRs, GCWR and max. hitch receiver wts. to consider, but probably not the issue you'll face first.
You're still at the point of guessing about a lot of things. I agree you would probably need 1200 lb spring bars, but unless you know the actual tongue weight, I would wait before ordering the bars. You don't want the bars to be undersized too much or you can get excessive bounce in the rear of the trailer (BTDT). If the bars are too undersized, you won't we able to "wind" them up enough to transfer wt. to the steer axle. That's why they call them "spring" bars...
Also, not sure why you need airbags. If it's because of rear end sag, then you haven't got enough payload capacity. You should be able to start your WDH setup by having the hitch ball higher than the trailer coupler (with level trailer) by about 1" to allow for settling of the rear of the truck. If the rear of the truck sags too much after getting the settled height of the front fenders right after hooking up, then your trailer is too much, or truck too little.