You could get by with a 1/2 ton on that size trailer but for your intended use I'd really recommend a HD model. Your preferred flavor 3/4 ton or 1 ton. For $45k you could even squeeze into a diesel if you keep the options limited, and even though your trailer size doesn't require one a diesel would give you an effortless towing experience with considerably better mileage and range.
I tend to agree with the others who have stated there's not really any downside to HD trucks versus half tons but there are a lot of upsides.