Truck will be fine.
Focus more on trailer prep. Mainly tires. Check condition and date codes. If they're dry rot and 5+yrs old, go buy new ones. This includes the spare tire. Next, wheel hub bearings. If you don't know when the bearings were last repacked, do it now. And finally, lighting. Make sure all your lights function. Usually while hooked up with the hazards on and parking light switch on you can test all functions at once. If the trailer plug or harness is shoddy, replace it.
There's nothing worse than being on the side of the road with a roasted bearing, blown tire, or no trailer lights at night.