IMHO you should replace your truck tires with LT tires. After buying my Tundra, I had to buy tires in a hurry because one tire had a bubble on the side wall and we were leaving on a trip (without the trailer). So, all I could get were P rated tires. We weren't doing much camping with our old trailer at the time. Well, after a period of time, we sold the old trailer, bought the new one and started camping in the new trailer. On one trip, I could feel the truck moving a little bit...the way I knew it shouldn't. After thinking about it, I decided to replace the tires with LT tires and the difference was very noticeable. And with the LT tires, you can inflate them to a much higher PSI....I like to inflate the rear tires to 65 PSI when towing. An added bonus was better gas mileage with the LT tires...1-2 mpg depending on conditions.
Otherwise, inflate your tires to the maximum 44 psi. Air temperature will make a big difference in tire pressure, which is why you have a adjust by the weather season or location.
I just broke down an bought a TPMS system for my trailer tires and rear tires on the truck. We're on our first trip with the system installed and it's really nice to be able to continually monitor the tire pressures and know that I'll get a warning if the pressure drops, if there is a leak, or if temps go too high. The system wasn't cheap, but less than typical repairs if you have a blowout. And, I can turn on the monitor before hitching up and see if I need to get out the compressor without having to walk around with the tire gauge and check each tire.