A domestic novel, also called a sentimental novel or women's fiction really reached its heyday from 1820-1865, though there are examples reaching back to the mid 1700's. Pride and Prejudice was published before its heyday in 1813, but Jane Austin was known through her letters to be influenced by Samuel Richardson, who was one of the forerunners in the genre.
Pride and Prejudice does focus primarily on emotional matters, which is the hallmark of a domestic novel. Lizzy fits the "practical woman" template, and does fight for self mastery through the novel and does make a marriage, all of which are typical of a domestic novel.
However, Austin's Sense and Sensibility is considered to be a more pinnacle piece in the genre, due to the witty, almost satirical version of the genre.