If you have the trailer heavily loaded, you might want to consider an auxilary tranny cooler, these look like a little radiator, and mount in front of the radiator. You also might want to consider an additive for the tranny fluid, there is one ( forget its name ) that many tranny shops use ( I think it is "Lube-Guard").
Unless you are pressed for time ( doesn't sound like it ), I would not suggest driving straight through, fatigue highly increases the chances of driver error, causing a wreck. At each stop, do a walk-around, check tire pressure, fluids, etc. Be sure to check trailer tire pressure, and make sure the trailer hubs have been greased. Check tongue/ball ( sounds kinky ). Check trailer lights. Make sure battery cables are tight and clean, especially the ground wire meeting frame. This is a good time of year to travel, heat is hard on loaded vehicles.
Should have no problems.
Mark