While a 2005 and newer F-350 SRW will have a 11,500 pound GVWR and carry about 3,500 pounds of total between cargo, passengers and options, the 2004 and earlier F-350 SRW will not have nearly as much GVWR.
I think that your truck will have a limiting 9,900 pound GVWR, and a curb weight around 7,000 to 7,700 pounds, depending on cab style and options. The 7.3L does not help, it is about 600 pounds more than the V10 or 800 more than a 5.4L.
Your truck should be fine with a 1,500 pound hitch weight of a travel trailer - but most fifth wheels you would need a 7.3L with dual rear wheels, or the newer ones with SRW. Even a F-250 after 2005 with a V10 will have a 10,000 GVWR (100 pounds more than yours) and have a curb weight less than yours.
If your F-350 is a dually, then you will not have any problem with a fifth wheel and a 2,500 pound pin weight. Much more than that, and even the older dually can get overloaded. The 2005 and newer F-350 dually has about a 5,000 pound cargo rating, even up to 5,700 pounds when there is a basic package (not the Lariat). Lariat can add a few hundred pounds of optional sound deadening, leather, and other things.
So is this post so that you can convince yourself or the better half about the need to get a newer truck or dually? The 2011 F-350 SRW will work fine with the load that you want to tow.
You can get information about the towing capacity of trucks at this site. It will show all years from 2004 on.
http://www.fleet.ford.com/towing-guides/ Good luck!
Fred.
