One thing you must consider about this type of pump is if it can handle pumping at higher than normal pressures for extended periods of time. Most of these pumps are meant for pumping water unrestricted and will bog down or overheat if to much restriction is placed on the output. With that said, there are certain pumps that are made for this use and have higher pressure output.
I have a small 1" Honda water pump that I use for watering my garden and it works great for powering 3-4 standard sprinklers. It isn't designed for real high back pressure use, but better than most. I have to run it at 3/4 throttle to keep it from lugging, since it can only push so much water through the sprinklers at a time. With more sprinklers it could probably be run full throttle.
As for your F-250 hauling 3800lbs, that all depends on how it is set up (year, GVWR, spring package, etc). There are many configurations on these trucks that can greatly affect the payload. Some F-250's have a light GVWR and payload capacity closer to an F-150, others are closer to an F-350. I have an '88 F-250 with the high GVW package, factory overload springs, etc and 3800lbs would be a pretty good load, but not overloaded. With that said, my father has a '99 F-250, same GVWR but lighter springs and no overloads, it would be riding on the bump stops with that much weight. If you are worried about it a small trailer would be a good option.