I have towed a 10K trailer for over 7 years with my truck. With a stock truck towing a 10K trailer it well be noticed but it was built to handle that kind of load 24-7, so no worries.
With the new transmission make sure you get a tranny temp gauge. Even with a stock truck even a tranny can get hot and heat kills transmissions. You don't want to fry that new trans. At least with a tranny temp gauge you can pull over and let it cool down if it gets too hot.
If you are going to put in a chip of any kind, make sure you do the required supporting mods as well. Intake, exhaust, wicked wheel(or ATS compressor housing) and gauges.
Keep Strokin'