Looking at what we are calling for here my recommenation would be:
Stick with the 3/4 ton truck. If the truck is being bought for the sole purpose to haul a horse trailer, the 3/4 ton is the way to go.
While most (and believe me, it isn't all) 1/2 ton trucks are capable enough to haul a 6000 lb trailer, they will be pushed out closer to their maximums than a 3/4 ton will. The 3/4 ton gets you heavier duty brakes, suspension pieces, and LT tires rated for decent loads. In general, all around more capable and competent package for trailer towing that brings an extra margin of safety. Also don't forget how many people may go into the truck. The 3/4 ton comes with crew cab tyoe options if need be, without reductions in cargo carrying ability or towing (at least less than a 1/2 ton).
With that said, gas or diesel? The usual tradeoff here is higher intital costs (generally 4-5k more at purchase) for diesels versus gasoline. The diesel will get you much better fuel mileage, especially while towing. Unfortunately, even this advantage generally requires 120-150,000 miles before break even is achieved against the initial cost. The counter to that is diesels hold their value better than gasoline engines, and generally will allow a 2-3k higher resale price. If you are going to buy it and drive it into the ground, then this means nothing. Also keep in mind what the operator and maintenance people are comfortable with. If the remiander of a fleet is gas, then perhaps moving to diesel isn't the right call. Some people just don't like the sound and smell of a diesel either, though this is less of a concern with modern diesels.
What I see here is a load that doesn't tip the scale all the way to a diesel, but makes it an either or choice. Especially with a manual box, the gas engines will be plenty capable to move this load. The diesels will very easily move the load too. I also notice we're talking Florida here, so the extra oopmh of a diesel to conquer long grades doesn't appear to be an issue.
As far as brands, in 3/4 ton trim, all three will do well. My personal preference here would be the Ford Superduty 3/4 ton equipped with a 6.8l V10. The 5.4 is a bit underpowered for this size truck, and the 6.8 V10 is a nice motor. It surprises a lot of people in its peformance. Fuel mileage unloaded would run around 14mpg, loaded closer to 11 mpg.
Dodge and Chevy also make capable rigs. I think engine choice in the Dodge would be the Hemi, but it doesn't have a long term track record yet. Chevy/GMC are also capable, but I am not a fan of the 6.0 V8 (feels a bit gutless and revs like a motor more suited for an automotive application). That being said, plenty of folks love theirs. The 8.1 V8 in the GM lineup is also a bit of a gas pig.
In short, all three choices have things going for them. My pick would be a Ford Superduty F250 with the 6.8l V10.