As others have said, higher RPMs isn’t a bad thing. The engine Is just getting into its power band. It certainly isn’t going to hurt it.
If you’re looking for an excuse to upgrade your truck, here is your chance. If you’re concerned about longevity of what you have and you don’t really want to upgrade, there is no reason you have to with your current trailer.
If you decide to upgrade and stay in a 1500, I’d skip the 5.3 V8. The perceived work (high RPM will be just as bad in that truck). Go 6.2 if you are staying with GM. If you really want to avoid the high RPM, your best bet is switching to Ford and going with the EcoBoost. I use an Expedition MAX to tow my 7000 pound boat, and it virtually never is running above 4000 RPMs.