It seems the answer to the opening post is "at least 120 years ago".
Farther than that!
I had time to do a little more searching on Google Books and I can now confirm that the use of
woman as an adjective (specifically in the phrase
woman doctor) goes back at least as far as the 1890s and 1880s.
It now looks to me like 1880s are when the term woman doctor became a recognizable part of the US and British vocabulary. Partly that's because I did not turn up any examples of the phrase in books from the 1870s, 1860s or 1850s but did turn up a good number of uses of the phrase in books from the 1890s and 1880s.
That doesn't mean people weren't using the phrase earlier than the 1880s, since I'm only able to search book text rather than what people were saying to each other in conversations back then, and I'm only able to search book text of books which have been scanned into the Google Books archive. There are probably many older books which aren't in their collection.
But there's another reason why I think the 1880s are when the phrase
woman doctor became part of the common vocabulary. While the history of doctors who were women goes back a good bit farther, the 1880s were when enough women in the US and the UK were allowed to study medicine, receive medical degrees, be licensed as doctors and establish medical practices for people in the US and the UK to have occasions to talk about this fairly new social development.
There were a number of interesting-looking listings of books and medical journals published in the 1890s using that phrase which my search turned up, and I hope to transcribe and share some of those passages in a future post. But that takes more time than I have free at the moment, so for now I'm simply going to share some content from two 1880s books. The first is from a novel in which the subject of women doctors comes up; the second is from a non-fiction book about the many new roles (including doctor) which women were able to take in the literary and business world of the time.