That trailer is within the tow rating of pretty much any full size truck on the market if it only weighs 4,500 pounds. If that's the advertised dry weight it likely weighs more than 1,000 pounds over that.
You certainly don't need a diesel. Just about everything will have an automatic transmission. If it's got 5 or more speeds it should be just fine. Preferably with a tow/haul mode.
I've had excellent service from numerous GM trucks over the years. A GM 1500 or 2500 would work just fine. The 5.3L or 6.0L are both excellent reliable engines. Just get one new enough to have the 6 speed transmission. 2009 and up I think.