BC282 is right on, and a tandem is desirable over triple as mentioned, and you can do that with the 16" wheels at a load rating to get you to your capacity. We looked at this subject in depth on trailering a 282 as well. You'll want something in the 12-14K lb rating. Better over-rated than under. You will be about 12K lbs on a trailer. These types of trailers are bunk trailers.
Don't forget to install a heavier hitch on your truck as they generally install a 5-7,000 lb rated unit. Just make sure everything is rated for your towing load, like the pull bar and ball. And make sure your trans has synthetic ATF in it if doesn't already.
I have a RoadKing which is a decent trailer, and I think they have a factory in Miami. They do have a ton of dealers in FL. The problems I've had with my trailer aren't really related to the manufacturer, but trailers and saltwater make for lots of little problems. You can shop their site for the various ratings and setups:
www.roadkingtrailers.com This is prolly the model that would work: RKAV 30-32TB It's a torsion axle tandem, with 16" load range E tires - 12,000 net carrying capacity.
Magic-tilt always seems to come up on the top list for aluminum trailers.
If you're up to modifying a trailer to fit, you might find something used that a boat mover is giving up on, they do come up for sale from time to time. They are harder to sell for the bigger boats. I've seen a couple of used ones out here in the $8-$10K range.