I had a WW FS2600, it is a very heavy trailer, much heavier than the stickers say it is, I had a 250cc quad and 4 dirt bikes (2 adult, 2 small kids) and full of water it was close to 11,000lbs
Now that being said, my buddy had the same trailer but towed it with a 2500hd with the 6.0 engine and it worked, towed pretty slow up hill, it was more stabile than mine towing with an Excursion, I don't know the differences in the 1500hd and the 2500hd, it is worth looking into but my gut tells me you will be buying a new truck.