If I were you, I'd go to a scale and determine your actual payload capacity by subtracting the actual wt. from the GVWR on the door jamb sticker. We have an F250 and the actual payload capacity is 1800 lbs which is much less than what the figure on the sticker says. I would also weigh your trailer when you get it and find the actual tongue wt. and GVW. You want to ensure your WDH bars are the correct rating and often the dry tongue wt is way less than actual.
If you have over 1200 lbs of tongue wt., you want to consider the weight of passengers, pets, groceries and other camping stuff in the bed. That can easily add 400-500 lbs or more. Some say it doesn't matter if you overload your TV on payload or axle ratings, but I'm not one. If you really have closer to 1500 lbs of tongue wt., you could be overloaded.
If you tow without a WDH, your front end could end up being a little light and may not handle as well. You don't want to find out the hard way in a panic maneuver or stop. Being overloaded on top of that won't help either.
Technically you may not really need a WDH hitch for that truck and trailer, but it would make for a much nicer and potentially safer driving experience. We have a Reese DC WDH towing a 29' trailer just under 7,000 lbs. I wouldn't dream of towing without the WDH. The truck drives straight as an arrow on the freeway and there is no sway from wind gusts or passing trucks.