I would not pull said trailer with.My now sold dually crew cab, OR my class 6 26K gvw dump truck. Why, trailer is unsafe. Probably not enough hitch weight, tongue too high vs level to slightly down.
EVERY trailer that has swayed on me, was too light in hitch, and or too high on the tongue. All started in mid to upper 50 mph range.
Seen tandem dual trailers sway behind tandem dual trucks, had an 8k trailer behind my dump truck sway.......A bigger truck WILL NOT solve the OPs issue!!!!! Any one who thinks so, is wrong. It might help, it will not fix the underlying issue to cause the trailer to sway!!!
Marty