I googled the Elkmont and only found one size, a 24' single axle, is that the one? If so, you can do it but need to be careful. The T4R has a short wheelbase which makes it prone to sway and a single axle is only going to compound that problem so some sort of sway control will be a must. Dry weights mean nothing and don't go by what dealers tell you. Plan on adding at least 500lbs for options like AC, water heater, propane tanks etc which are not included then add your camp gear. For comparison my 19' hybrid has a dry weight of 2800lbs but lightly loaded for a family of 4 it is 3800-4000lbs with the water tanks empty.
The dry tongue weight of the Elkmont is listed at 540lbs which is pretty heavy and exceeds the limit of the stock x-member mounted hitch. You'll need to upgrade to the frame mounted weight distributing hitch from the V8and use a WDH system such as the equilizer (with built in sway control).
I've posted before about my experiences towing with my '03 V6. Didn't even notice the pop-up, then upgraded to the hybrid. Well within all towing limits and it handled the weight but the drag resistance from the frontal area was the killer. Matched with the V6s 4 speed it was a struggle on the highway. If you're only going short trips you'll be fine, get the trailer weighed and make sure you are properly equipped.
Happy camping.