This is similar to my situation. 7200 Gross trailer weight and we go down the road right at 6500. I have stopped and weighed more than once. It is going to come down to what you plan to take with you. You can load some stuff in the trailer but the rest will have to go in the bed of the pickup. It is only the two of us now and we usually take along a generator and some extra water when we boondock but other than that, not much heavy stuff.
The V8s today are designed to run at high RPM so don't let people scare you about getting over mountains. I can climb almost any hill at 60 in 4th at 3K RPM when needed.
Keep the trailer light and you should be fine.