Rather to send you to yet another website with more confusing/conflicting information, or telling you to "weigh it" (How can you weigh it without buying it first, and if you buy it and it's too heavy, then what? Then, you have to tow it to weigh it, but you can't tow it until you have it weighed, so now what do you do?)...
First thing you need to do is figure out the tow rating for YOUR vehicle. Is that 6000lb rating for YOUR vehicle, or the "if properly equipped" vehicle? Manufacturers like to pump up their products by advertising the maximum capacities even if they conflict with each other, or require special equipment.
Your vehicle's tow rating will be in the manual. Somewhere in the middle of the manual there is a section on towing, which will have charts that you can use to figure out the tow rating based on what engine, what axle ratio, what body type, what tow package, and what trim level you have.
If your actual tow rating is anywhere near that 6000lb mark, you should be just fine with the trailer you've chosen as long as the weights for the trailer are anywhere near accurate. That trailer should load out somewhere in the 4500-4800lb range, with a tongue weight around 600lbs. That should be well within the ratings of your vehicle if what you've said so far is correct.
With a 600lb tongue weight you will need a weight-distributing hitch. That is right at the limit of a class III receiver's weight-carrying rating, but more importantly, it will pull a lot of weight off your vehicle's front wheels, causing handling and braking issues. The primary purpose of a weight distributing hitch is to return that weight to the front wheels so your vehicle handles and stops properly.
