I would say yes even without the dually as 10k should not be an issue for a 350/3500 SRW.
I am a far cry from the weight police crowd but my personal opinion and only my personal opinion is 10k is too much for any half ton regardless of its tow rating or payload rating, that could approach twice the weight of the tow vehicle. 350/3500's additional weight, suspension, brakes etc will certainly help add to the stability and safety factor. I realize that some 1/2 tons have higher tow ratings than 10k but a travel trailer/fifth wheel especially 38 feet long is going to behave differently than a flatbed trailer loaded to the same weight with say concrete bags or whatever equipment unless you have built a big box around it. I know on my 3500lb equipment trailer loaded down with a 9000lb skid steer tows better than my fifth wheel (10k lbs) even though it weighs 20% more.