I believe your 2000 F250 has a GVWR of 8800# per the sticker on the driver's door jamb. The truck in road ready form will probably weigh close to 7000#, maybe a little less. This will leave you a cargo or payload capacity of 1800# (8800-7000). A typical 5er will have a pin weight around 20% of the trailers GVWR. So a 12000# GVWR will result in a pin weight of about 2400# when fully loaded. This is about 600# over the rating for your truck.
The only way to know for sure is to weigh the truck in travel trim with all normal cargo and passengers and add 150# for a 5th wheel hitch.
GVWR - loaded truck = max loaded trailer pin weight.
GCWR - loaded truck = max loaded trailer weight.
The problem with a 3/4 ton truck is the limited payload capacity and the higher pin weight of a 5er. The truck can pull plenty, but will reach the GVWR long before you reach the GCWR.
You would be able to pull a larger TT than a 5er with yor 3/4 ton truck. A TT will typically havea hitch weight of 10 to 15% of the trailers GVWR.
Dry weight is a useless number as it is based on a base trailer and usually does not include any options such as A/C, microwave, batteries, awning and certainly no camping supplies or water or propane. The loaded weight can easily exceed the dry weight by more than 1000#.
You will see lots of folks pulling larger 5ers with a 3/4 ton truck. They were misinformed by the dealer, do not know anything about weight ratings or simply do not care.
A 3/4 ton truck can be used to pull a 5er, but you do need to watch the critical GVWR and payload issue. You will pretty much have a 3/4 ton truck at it's limit on GVWR with a 30 to 32' 5th wheel trailer.
Oh, by the way, glad to have you visit iRV2 and hope to see you often.
Amateur Radio Operator (KE5DFR)|Full-Time! - 2012 6.7L Ford Crew Cab Dually -2013 HitchHiker Champagne 38RLRSB - Travel with one Standard Schnauzer and one small Timneh African Gray Parrot