I towed a pop-up camper with a Chevy Lumina Mini-Van for over 6 years. The entire weight of the pop-up was around 1500 pounds. Add the weight of our passengers and supplies, propane and all, it probably weight about 2500 pounds. It towed just fine. Eventually, we towed with a 1500 Chevy Suburban, and the Mini-Van lasted for another 5 or 6 years. We finally traded the van for the "Cash for Clunkers" program, only because the air-conditioner was the old-style and couldn't get it fixed with spending a fortune. Time for a new vehicle.
I think towing anything much heaver would have been awful on the van, the transmission, and everything else though. I think the trailer you are considering is REALLY pushing your van. It will tow it, but for how long before damage occurs. I think you really need to think smaller trailer if you are unbending on your choice of tow vehicle.