Paul,
If a 600cc, it would be a G/31, G/32, or G/33 depending on the year it was made (1931-33.) If a 500cc, it would have been a F/31, etc. It was Douglas' sporty road model offering of the time. It was not sold as a racing machine, but the engine was based on and used components and modified patterns of the recently obsolete Dirt Track models.
The only oddity is the front forks. Per catalog illustrations, the F/G models used a front fork very similar to the Dirt Track models, with concessions for brakes, mudguard, and attaching a headlamp that the Dirt Track machine did not require. That is not the fork fitted to this machine, which is more like the forks fitted to other Douglas road models of the1934-35 era. It may be this is a 1933 model and that is what they fitted that year when the old stock of Dirt Track forks ran out (perhaps even running out in 1932.) It also has the large barrel compression spring centrally located, which featured from 1933-34 onward. Also supporting this theory is I do not know of any other brazed lug construction fork with the brake drum on the right that would also have the four point head lamp mounting. The side valve models and the OHV models of 1934-35 had the brake drum on the left. OHV models up to 1929 had the brake drum on the right, as did the F/G31. But they did not have the four point headlamp mounting; that came after the twenties. In other words, these forks seem unique.
I have not yet seen a period published photo for a 1933 F/G model, and indeed the factory was in severe financial distress that year and output was almost non-existent. Only magazine adverts indicate they did, or intended to, produce the F/G in 1933. The F/G model was significantly redesigned for 1934-35 and became the OW/OW1 models.
-Doug