|Yale Center for British Art, Paul Mellon Collection (PD)|
The definition of a shooting or gun dog is one that is bred to help retrieve game, usually birds. They may be retrievers, flushing dogs, or pointers: they go fetch the bird, or they run up and make the bird fly out of its cover, or they point out exactly where the bird is hiding. I can't tell which sort these are (Setters? They are big enough) but they are a handsome pair.
George Haugh executed this piece; I do believe this portrait by Benjamin West shows the same woman 10 years later.