Hi to you. Welcome to the forum.
I have a similar truck (but 6.0 diesel engine), towed similar (and larger) trailers, and believe you will be fine. Hopefully there will be folks here with your same engine and we'll see what they have to say.
If you haven't already, investigate weight distribution (WD) hitches and anti-sway. I've used the Equal-i-zer brand 4-point hitch for years and have been very pleased with it.
Sherm & Terry w/rescue Eydie (min Schnauzer) & Charley (std Poodle)
2015 Jay Flight 27RLS, GY Endurance (E), Days: 102 '15, 90 '16, 80 '17, 161 '18
2006 Ford F350 PSD, 4WD, CC, LB, SRW, Cmpr. pkg, Equal-i-zer 4-p, ContiTrac TR
Full timing: Some will think you're crazy, some will be envious, just enjoy the freedom!