A few things to remember when you get your boat/trailer combination. Make sure you add the weight of the trailer (empty) and the weight of the boat together. Many folks forget the trailer weight when figuring their towing capacity. Also, what ever weight you are told the boat weighs will be the "dry weight." That means no fuel, no gear, etc. You can easily add another 500-1000 pounds of weight when your boat is fully loaded. Factor in all those numbers and the tongue weight before you buy a boat.
The good news is that the weight of the boat/trailer you are looking at will most likely be within your towing capacity. Based on your description of your truck its really not outfitted for towing (small engine, high gear ratio, etc) so it may not have a tow/haul mode or built in trailer brake controller. That doesn't mean that you cant tow, its just a little more work on your part.
Don't drive too fast and make sure your truck brakes are always in good condition as towing will increase wear and tear on your brakes.