I have an 02 F 250 crew cab 7.3 diesel 4x4.
The towing specs on my truck and yours are actually very close.
I have a 3H LQ that is 28' long, and my truck does fine with it. I checked all the numbers and fully loaded it is approx 14,000 lbs, which is just about the max of what I should be pulling with my truck. Granted I dont pull in the mountains or anything, just in some small hills.
That said, our next big purchase is going to be an F350 dually because I think the added stability etc is a little safer for a trailer that size. We just happened upon the LQ and it was too good a deal to pass up so we went ahead and bought it before we had really planned to. I have another trailer, a 2h straight load GN, that i use most of the time and just use the big trailer if I need the LQ.
I still have all the stuff from when i bought mine with the booklet with all the towing specs, I'll dig it up when i get home and post something tomorrow. But you should be fine, you can pull a little more than I can, and the F350's have the beefed up rearend, which is why I added springs to my truck when i got the big trailer.
YOu can also take the trailer to a truck stop or an inspection station and have it weighed on their scales and see how much it weighs.
"Perhaps the final test of anybody's love of dogs is their willingness to permit them to make a camping ground of the bed" -Henry T. Merwin
More than likely, the sticker on the trailer that says 12K is the GVWR, not the empty weight.
IMO, this is way too much trailer for a SRW truck.
You have about an 8,000 pound truck empty with a GVWR of 9,900 pounds. That leaves you 1,900 pounds for trailer tongue weight, people, dogs, coolers, etc. So figure about 1,500 pounds for the trailer tongue. GN trailers put 20-25% of their weight on the truck, so even at the low end, that would be a 7,500 pound trailer to stay under your GVWR. The other number to watch is your 20K GCWR. That would put you in the 11,500 pound trailer range to be below this number. Clearly the 9,900 pound GVWR is the deal breaker. That number did not change appreciably until the 2005 model year.
We pull a very large Jamco 2+1 (no LQ) with our 2005 dually, and I would not want to pull anything larger. We are right at 21K combined with 2 horses and a weeks worth of supplies on board. I would love to move up to a 450 at some point.
Do check your numbers and check tongue weight vs the GVWR of the truck. My 250 on the quarry scale weighs 6860 with an empty bed, so your 350 should be a little more than that. 4H with LQ sounds pretty big and heavy....