When I spot likely pictures online I try to do a little research which mostly consists of dragging them into Google images and having a quick dash at wikipedia. I had a bit of trouble tracking this one down but I believe it to be called 'Gift' by Marguerite Gérard (1761-1837). The page I found it on dated it to 1788 which surprised me a bit as these high-waisted dresses didn't come in till the late 1790s. I assume the gift is the dog, sent with a letter from an admirer.
I'd never heard of Gérard before but apparently she was much admired in her day and was the sister in law of the celebrated artist Fragonard, whose house she lived in from the age of 8.
If you're interested in the history of women's fashions, here's a fascinating website which shows them year by year from 1784, illustrations taken from fashion plates of each year.