Thanks to everyone who helped me to date Edouard Vuillard's painting. The date on the label was ca. 1890 but this didn't seem right for a number of reasons. In 1890, Vuillard had a different sense of space and used paint in a different way. Considering style and technique alone, the work was more similar to his works of the first decade of the 1900s. On the basis of your suggestions of 1908-1910, I image-Googled "1908 hat" and found a photograph of a woman with an almost perfect match to her hair, hat, and jacket.
Further thoughts on the subject are still welcome, of course!