This is Johann Zoffany's (German, worked in England, d. 1810) portrait of Archduchess Maria Amalia of Austria, Duchess of Parma and Piacenza. Zoffany was a Neoclassicist, which normally would make for a more stripped down presentation and color, but I think this is just a poor reproduction. I can't find the date on this, but it might be 1772-79, during Zoffany's extended stay in Italy. He was very fond of a deep red for a Neoclassicist, though. Just look at that chair.
So - do you see the dog? No? Look down in the lower right hand corner. Surprise. That's why I chose this image today; it's unusual for its time in the almost subtextual use of the dog. After all, isn't the dog-in-the-portrait usually one of the first things you see? One of those trappings that points up the essential humanity of the great person being portrayed? Right. Why is that dog sticking its nose out so warily from the side?
My first guess is that the dog so perfectly mirrors the wary, sidelong look of his mistress that it's humorous, and Zoffany was said to have a bit of an attitude and humor to match. Secondly, perhaps Zoffany saw something embattled in this woman that he couldn't help but portray. A daughter of Empress Maria Theresa, from whom she was largely estranged most of her adult life, Maria Amalia was married to the Duke of Parma in a court that seems to have been a bit of a mess. She had a taste for power, and tried to exert it since her husband didn't care to step up. Nothing seems to have been easy. No wonder she - and her faithful pet - are giving you the onceover.