I'll echo the rest on the NO answer. My trailer is about 32 feet bumper to ball with a "dry weight" of 6425. My Suburban is a 3/4 ton with the 6.0 and I would say I am at the comfortable limit of my rig. It handles fine, but I had to upgrade the aux trans cooler to a 40k unit to keep the trans happy. I also upgraded the front brakes to the PowerStop z36 setup.
The last year of the 3/4 ton Burb was 2013, although you can get a 1 ton through a fleet dealer if you know the right guy...but expect to pay $75k+
Personally, I'd go with a pickup. We went the SUV route because my daughter gets car sick and having air behind her seat and not a wall helps tremendously.
Side note - When I ordered our trailer, the specs stated 5800 but it arrived with a 6425 sticker...and magically the MFR updated the specs to the heavier amount months later.