The 2500 burbs sit higher in the rear so they level out when you put a load in the back or on the hitch. What you don't want to do is offload the front axle any.
First thing I would do is measure from the ground to the front wheel wells unloaded, then add the trailer and be sure you are not gaining height in the front, indicating removing weight from the front axle.
Assuming OK there and it sits level, you should weigh the tongue to be sure it's within the weight carrying spec of the receiver (500 lbs). You can weigh the tongue with a bathroom scale, google will get you instructions on how-2.
It's unusual to NOT need a WD hitch with a travel trailer and an SUV, but it's possible. Check your heights and weights and decide. It's not going to help sway control, and since you don't have sway issues, there's no reason to use one if you don't need one....unless it makes you feel better :B