I am not an expert, but I would do some checking before buying a hitch rated at 10,000/750. for your application. There are some downsides to such a stiff hitch on a lighter trailer, which may be why many manufactures also offer a 6,000 or 8,000 rated hitch. Others may want to weigh in here.
2012 Chevy Silverado 1500 with factory brake control
Equal-i-zer 600/6000 hitch