DennyF, I have a few questions for you:
1. Is the 11,000lbs weight of your trailer the max gross weight of the trailer (ready to go out and play with all your gear loaded) or is this the empty weight of the trailer? There is a sticker on your trailer (usually on the tonque of the trailer or the front left corner of the body of the trailer) that states the Max GVW.
2. What is the cab and bed configuration of your truck?
3. What is the loaded weight of your truck with all of your gear in it ready to go camping (don't forget passengers)?
If the tires on the truck say they are a Load Range E they are sufficient for your truck. On the drivers door jamb of the truck is a sticker that has the VIN #, GVW, Max GAWR (Gross Axle Weight Ratings) and tire pressure for the front and rear axles. Look up the tire pressures on this sticker and I'll bet they say 55 psi for the front tires and 80 psi for the rear tires. This is what your tire pressures should be set at to comply with Ford's ratings for the truck.
First....Since your truck is a 2004 F-250, it has a Max Gross Vehicle Weight (GVW) of 8,800 lbs. Weigh your truck on a scale, preferably with it loaded (don't forget your fifth wheel hitch!!!) as you would for your trips. Quarries, feedstores, metal recycling yards, and truck stops all have a scale you can use for free or a small fee. Take the scale weight of your truck and subtract that number from your truck's GVW. This will tell you how much payload you have left in your truck for the hitch weight of the trailer.
Now you need to get your trailer weighed preferably empty and loaded so you know how much gear you have on your trailer for wiggle room and so you can calculate your hitch weight of the trailer. You should have 20-25% of your trailers total loaded weight on the hitch. This hitch weight will cut into the amount of payload you can carry in your truck.
Now, moving on....Your truck has a Max Gross Combined Weight Rating (GCWR) of 20,000 lbs. This means your truck, trailer, cargo and all occupants of the truck should not exceed this weight.
This should help you make a decision about the limits of your truck and whether you need more truck. My personal opinion is that if you need more truck for that trailer you will be better served finding a nice dually instead of converting your existing truck unless you really like you truck and want to go through the hassle of the conversion.
Here is a link from Ford that helps you figure things out, just scroll down to the 5th wheel table on the bottom.
https://www.fleet.ford.com/showroom/rv_trailer_towing/2004/2004RVTrailer_F250_350.pdf