While not that common, parts for the 1930s models are about; but it does take patience. It would not be so bad were it one of the big side valve twins, as they were reasonably popular by Douglas standards, but the lightweight twins were losing out to other makes.
What you really need to do is start is start educating yourself as to which bits remained unchanged or very similar for the models immediately preceding and following the Terrier. For instance, a Terrier is nothing more than the previous year's A31. It might have carried through into the following year, but Douglas production in 1933 is a very murky field. The B31 was a sump model, so it has, of course, as sump and also a different frame. The crankcase is machined accordingly, but much of the rest of the engine shares the same bits as the A31, and so the Terrier. Also a lot of the smaller cycle bits would be the same, but by comparing the catalog pictures you will see that the different frame called for many subtle differences so careful study is warranted.
In 1932, the B32 was the touring and overseas version of the Terrier. It seems to have lost its sump, so the engine is likely even more so identical to the Terrier and it looks like they share a frame of similar design. But it has drop center rims and low pressure tyres, larger petrol tank, and continues to use the old style rear carrier rack. Also it has removable plate heads, so the cylinders, inlet and exhaust manifold change accordingly. Also see the reference tables
here as a place to start picking up the year by year and model differences/similarities.
The C32 Bulldog in the Reference section
here is nearly identical to the Terrier in all respects except for the cylinders having the plate heads per B32, and being bored out to a larger capacity.
Things like brake parts as fitted to your Terrier were used on virtually models from 1930 till 1938.
It takes a while to figure out what is what, so you will just have to post questions as you work your way through the pile. At least you are off to a good start as you found the right forum to ask such!
-Doug