I don't have that trailer or that truck, it may be a well balanced setup (even if too heavy) and tow just fine (no sway). That would leave you with some power issues (just go slower) perhaps and some braking issues (make sure to leave plenty of room and keep your trailer brakes properly maintained). We towed too heavy with our 2008 Yukon XL Denali for 3 years, within the specs but with P tires. We had plenty of power but just felt pushed around too much. We upgraded tow rig to 2500HD and had no issues (until we upgraded trailers and then had to do hitch/WDH upgrade to get back stable).
If you are doing short trips closer to home, then you might want to look at dedicated tow rig, pick up a used older rig cheap until you can upgrade primary rig.