Carl,
From what I can work out Douglas were not released from their WW1 contract until sometime in 1919. So new bikes, "W.D." models of the "veteran" style frame, tank and fork were still being made in 1919 (and later to use up surplus parts.
An easy way to check to see what forks you need might be to measure the diameter of the receptacle for the head lug ball races in your frame (part 674D for a "veteran" frame and 1586D for a "Vintage frame")
674D = 1 9/16"
1586D = 1 23/32"
The veteran steering column tube is 1" diameter. The TS one is 1 1/8" and may not even fit through the steering head on the earlier frames (they don't on my veteran frame).
I have a supposedly (...on reasonably good authority) 1919/1920 tank and it is of the early "veteran" design, not the TS style, but has a "two blue panel" paint design like a TS rather than the "three blue panel" design of the veteran ones. The paint work appears to be original. So it could be that veteran style tanks were used in the 1919-20 period alongside the TS style but I cannot say for certain which style your frame may have had originally. If the frame only takes veteran style forks then one might assume it had a veteran style tank originally??
1919-1920 was a time of flux for Douglas changing over from the war effort to civilian effort and their documentation (i.e. parts books and sales brochures) doesn't appear to always reflect exactly what was going out the doors.
Cheers
Ian