I have the same truck, in SE trim. I routinely tow a 7000# Arctic Fox (provisioned, packed, watered, and ready-to-go weight) with the truck and it handles it well. The truck is rated to tow up to 9500 pounds in SE trim, up to 7500 pounds in any other trim. The difference in the ratings in that year was all in the tire-and-wheel combination. If you have truck rubber on it, you can tow as much as an SE.
This has been the subject of much debate in some forums, and it comes down to this: brakes, transmission, rear axle (from bearings to springs), shocks, frame, are all the same on all models. ALL Titans have a separate transmission cooler; it was designed-in when the trucks were designed. NONE are without a transmission cooler. ALL are capable of the full towing weight of 9500 pounds, provided you have a minimum of 18" wheels and heavy-duty rubber.
There was a Big Tow option which gave you a lower axle ratio, which changed *nothing* in regard to load-carrying and towing capability, but only allows the engine and transmission to spin faster at all speeds, resulting in better cooling.
There is a Tow Mode button on the lower center dash and some people think that means you have the Big Tow option. Not so. They all have that button, all years, all models. The one easily-findable, visible difference in 2004 was the presence of a transmission temperature gauge. You can't add that to a non-Big-Tow package.
As far as my particular opinion goes, after more than 9 years of experience with my particular truck and trailer, your truck will tow it, but I'd watch how much stuff I packed. You're starting already with 500# more weight (non-provisioned) than I have, all ready to go.
Technical info begins on page 308 HERE.Hope that helps.
(edited to clarify the two other responses)