When I weighed my k99 loaded ready to camp on my f350 srw, I was at 12, 000 lbs.
I have never seen a short box specific Kodiak, just shorter nose ones with east west beds.
They are well built campers, but anything but light. The guy who I sold it to put it on a short box f250 that had a custom flat deck on it that was 8ft long...I wouldn't be worried about supporting the back part of the camper, they will handle it, you can also leave the tail gate on for a bit of extra support. I can't speak to how the handling will feel.
Good luck!
2005 arctic fox 990 silverfox
2008 Silverado ltz drw duramax 6speed allison
1999 Kodiak k99 / 2008 ford f450 6spd manual. SOLD
2000 citation supreme SOLD
1989 camperette SOLD
1985 okanagan SOLD
1990 northern lite SOLD
1995 northern lite SOLD
1997 Kodiak k99 SOLD