You don't have
to have one, but...
Your tongue weight is going to be a good deal more than 180 lbs. The rule of thumb for reducing sway to something manageable is to have 12-16% of the towed weight
(gross weight when traveling) on the tongue. Dead empty weight (as advertised) of 2500 lbs would give you ~370 lbs of tongue weight and I'll wager your empty weight is going to be closer to 3000 lbs. The term "dry weight" is something that RV builders use to sell "light weight" units, not deliberately misleading, but, pretty darn close. Dry weight doesn't include the battery, the propane in your tanks, the awning and any other "options", whether mandatory options or not (like the microwave for instance).
In reality, it is far more likely that your tongue weight will be upwards of 400 to 500 lbs. Do you need a WDH for that load in your pickup? Probably not, but, IMHO, the truck will ride better and handle better if that tongue weight was distributed between both axles and not hanging solely off the back of the truck. There are a lot of folks that don't use one for that load, particularly on a pickup truck. For a while, I towed my 210WBS with my RAM 2500 with the HO Cummins Turbo Diesel. My tongue weight was right around 900 lbs. Well within the load limit of 2460 lbs for that truck. I used my Equal-i-zer WDH hitch. Weight distirbution hitches are adjustable...you don't have to use the full amount of bar or trunion leverage available on the hitch, just enough to level up the tow vehicle and spread the load over both axles and control the sway. The bar tension on the truck was less than half of what I used when I towed that same trailer with my Jeep Commander, but, I used it none the less, I just move the bar brackets down a notch and a half.
For the 160, you can do without it, but, I would probably go ahead and bite the bullet...how long 'til you trade up to a larger trailer? Never say never
I did and now look what I've got