Because they tell you you can tow it does not mean you would want to, flat trailer with rock for landscaping, ok. Tall wind catcher we call RVs
If you are on flat roads with no head wind... ok.
Most likely you will be at the edge of what it would do. If you decide to, try to get one that is as aerodynamic as possible.
Not looking to upgrade trucks I would try to go lighter. Like the Cougar XLite (Strictly by weight, I do not know quality).
Had a F350 v-10 that could tow 14k, tried it (in PA hills). Did not like it. Ran out of power on hills and was not a pleasant ride. For us, moved to the diesel then ended up upgrading trailer.
The second part as mentioned if you end up upgrading trailers you will want to upgrade your truck.