I have a buddy with the GMC 1/2 ton w/the 3.0 Duramax and this weekend helped him set up a mobile photo booth (his side business). This consisted of towing the photo booth (a renovated 1968 VW bus, similar in weight to our TJs) on a flat bed trailer that I'd guess weighed about what the one you plan to use does.
He recently traded in his 3/4 ton Durmax for the 1/2 ton when he sold his 34' toy hauler. I asked how how the 2 compare and he said that, while he loves the new truck for the improved mileage when not towing, after towing with both, the 1/2 ton does fine on short trips around town with the trailer/VW bus package, but for anything more demanding - either longer trips w/significant grade OR a heavier load to tow - he'd always take the 3/4 ton for better power, better braking and more stability.
If I were in your shoes, I'd lean toward a 3/4 ton, and probably one of the gas options unless you eventually plan to tow more freqently, much further, or much heavier.