I'd say you're good to go. We have a 34tbok, I think similar to size and weight of what you're considering, and used to pull with s f250 gasser. It handled it fine, but I did add air bags to keep things level and firm. The diesel will pull it fine, it's the pin weight you'd need to watch. If it were me, I'd go ahead.
We switched from a 28' 7000lb tt to our 13K + lb fiver and it's much more pleasant to haul
Joel and Teresa
2016 Sabre 34TBOK
2006 GMC 3500 CC LB DRW 4X4