I would, and as you can see in my avatar, I do. However, I do it cautiously and with the proper equipment. My T4R handles it ok, but it is not the ideal tow vehicle by any means.
The weights you list are likely far from actual. Dry weight means nothing since it does not include optional items in the trailer, or battery, propane etc. Empty weight is more important to know and is likely 4-500lbs higher than dry. Now add 800-1000lbs of your gear, food, clothes, water in tanks etc. You'll likely be closer to 6000lbs and a tongue weight closer to 700lbs, which quickly approaches or exceeds the T4Rs limits.
Now you're probably looking at those figures and saying to yourself "what's the problem, that's all within limits?" Usually the limiting factors will be payload and rear axle weight rating. You'll max these before reaching the stated tow limits.
You should go to the scales with and without the trailer to get some weights.
You'll still have to estimate since the trailer will be unloaded. First without the trailer, just you in it and a full tank of gas to get curb weight. Subtract that from GVWR (5710lbs) to get payload (what you can put in T4R). Max payload is 1215lbs. Now subtract passenger and gear weights and at least 100lbs for a WD hitch from payload number to determine what you have left for tongue weight.
If you can get the trailer on a test tow to the scales, you should load the T4R and confirm you are under the rear axle weight rating (3064lbs) and under the combined vehicle weight rating (12,000lbs).
If you can keep it within those numbers, you should be ok, with the right equipment. A proper WDH with built in sway is a must. At minimum an Equilizer or Reese dual cam. Better yet a Hensley Arrow (big bucks but worth every penny). A good brake controller (Tekonsha Prodigy) and proper mirrors are also important. You'll need to consider a few things for your T4R too. Stock tires are P rated, and too soft for towing that weight. You may want to consider installing air bags if you don't have the factory load levelling airbags.
My trailer is of similar size and listed dry weights. Loaded lightly I'm at 5500lbs with 660lbs on the tongue. I'm right at max GVWR and slightly over the rear axle rating. I have an aftermarket reciever which was reinforced more and use a Hensley. (have an Equilizer too and it did ok) You won't win any races, will struggle in mountains and stopp every 2 hours for gas, but if you take your time and leave lots of space it can be done safely. Hope this helps.