I think you should be close... probably okay depending upon how much weight you carry in your truck (not counting tongue weight)
The GVWR for the trailer, at 7565, means you should consider about 1050 lbs for tongue weight (14% at full GVWR). That leaves you about 600 lbs for you, passengers, and any other cargo you carry in truck.
Generally speaking, payload is the first spec that one exceeds. So, if you end up below payload, you should be good with all the other specs (tow rating etc).
I will say I pulled a 6800lb trailer with my 1/2 ton, and I personally wouldn't want to pull heavier than that, even if I had the payload capacity. It towed fine at that weight, and was within all specs. I just didn't think it would handle as well with any more weight.
Mike