Pick1, A quick web search just now came back with this one possibility for your 1 Ton. Nowhere in there does it give dimensions, but you should be able to call them and confirm that it fits or not. Hope it gets you what you need.
~ Dan 1951 Chevy 3 window 3100 Follow this story in the DITY Gallery "My Grandpa Carl's Truck and How it Became Mine" 1966 Chevelle (Wife's Hot Rod) | 2013 Chevy Silverado (Current daily driver) US Army MSG Retired (1977-1998) | Com Fac Maint Lead Tech Retired (1998-2021)
A little deeper searching turned up this company. Their website is really old and doesn't look to have been updated recently, but a web check of the company name/address "Bruce Horkey's Wood and Parts 46284 440th st Windom,MN 56101" came back showing they are open and seem to still be active. Their site does list bed wood available for your 1 Ton (see pic below snagged from the site), but my guess is their prices listed there aren't current. At least it's another one to call and see what they might be able to do for you.
~ Dan 1951 Chevy 3 window 3100 Follow this story in the DITY Gallery "My Grandpa Carl's Truck and How it Became Mine" 1966 Chevelle (Wife's Hot Rod) | 2013 Chevy Silverado (Current daily driver) US Army MSG Retired (1977-1998) | Com Fac Maint Lead Tech Retired (1998-2021)
I got my wood from them for my 51 GMC 1 ton 7 years ago. I had to drill the mounting holes, but it was a good kit.
Be aware of the mid year switch (51 I believe) from 9 boards to 8 boards.
1970 Chevrolet C10 Grandpa's -- My first truck -- In progress to shiny Follow the build in the Project Journal 1950 Chevrolet 1-Ton Dually "Ole Red Girl" In the Stovebolt Gallery More pictures here 1951 GMC 9430 1 ton dually--Shiny! | 1972 Chevrolet C20- Rusty- the puzzle box lid for the C10 | 1962 AMC Rambler American- my wife's Parts trucks- 1951 GMC 9300 | 1951-GMC 9430 | 1951- Chevrolet 1300
I'll second Mar-K. I used their kit for my '51 1/2 ton Chevy. The only holes I needed to drill were the outer boards where they bolt to the angle strips. The mounting holes to the frame were pre-drilled including for the offset washers.
Kevin 1951 Chevy 3100 work truck Follow this saga in Project Journal Photos 1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car) Busting rust since the mid-60's If you're smart enough to take it apart, you darn well better be smart enough to put it back together.
I have purchased from "Bruce Horkey's Wood and Parts 46284 440th st Windom,MN 56101" and was very pleased with the oak bed they supplied for my 1954 half ton. They brought my wood to their booth at "Back To The Fifties" in Minneapolis a few years ago. They charged a fee but saved save me some on shipping charges. Very nice vendor to deal with.
Been years ago....i bought a complete bed unit from Robert's Motor Parts in conn. I belive they still in business was very pleased with my '37 compete outfit.
At least it's another one to call and see what they might be able to do for you. 
