Forget dry weights, stay with GVW of the unit you're going to tow....Don't know if that specific truck will work that well for you...No way do you need a 1 ton to tow that TT with, but you may want to think about a 3/4 ton truck...IF you want to keep what you have, you may want to consider a lighter weight TT....Look on your drivers door sill and see if you can see what your trucks GVWR is as well as it's RAWR (rear axle weight rating)....but the 5.3 with 3:55 may not be happy loaded with family and loaded trailer...
Others may chime in and be able to help you more.