This is an interior wall in a bedroom closet in a house built in 1940 in the northeastern US. I suspect that the material is not typical drywall from other experience hanging things on other walls in this room (a threaded drywall anchor doesn't bite into the material), but on the other hand I don't see any sign of wooden lath anywhere.
The stud is 1 inch behind the surface of the wall (lighting is poor here, used a flashlight to help):
and here is what the debris from drilling into the wall looks like:
Can you have plaster this thick without the wooden lath material to support it? Or if this appears to be drywall, was this a more common thickness back then (I know 1/2 inch and 5/8 inch are common now in the US)?