I had a 2002 F250 2WD shortbed, that I pulled a 9000 lb, 30 ft bunk house. It would go anywhere all day (and night). It was a great combo. The early 00' model F250s had the same spring rates and suspension as a SRW F350. Only difference in published weight ratings was due to lesser tire capacity. Upgrade the tires and you basically had a F350 of that era. That's changed with the next gen of truck.
And as Cowracer (Hi Imperial from Edwardsville) noted. It was really easy to get a 7.3 up to today's level of power. I had mine chipped, exhausted, injected up to 425HP and 830 lb/ft. Roughly the same as my current 2011 F350 (400/800) and my 02 weighed 1000 lbs less. And all that cost me less than $3,000.
If your truck is stock, I'd probably look for 30-31 ft, under 11,000 lb trailer. A non-modified 7.3 will feel under powered with a 12,000lb + trailer.
2016 Coachmen Chaparral 390QSMB
2011 F350- CC, DRW, LB, PSD
2016 nights camped: 40