Pride and Prejudice might be analyzed as a 19th century domestic novel only with great difficulty. Let's first look at the characteristics and objectives of the domestic novel.
- deprived, friendless heroine
- penniless, forced to make her own way in the world
- dependent upon externals to take care of her, no inner resources
- through hardships, develops self-reliance and reasonable views of the world
- her self-reliance now brings good and happiness to her unsought
- expose the inherent goodness of human nature
- contradict Calvinist doctrine of human deprivation
- advocate feelings as the best guide to right and moral conduct
In their reliance on the inherent goodness of human nature and the power of feelings as a guide to right conduct, these novels were in part a reaction against Calvinistic doctrines that viewed humanity as inherently depraved. (Adapted from Nina Baym, Woman's Fiction. Washington State University)
I think it is clear that there is no overall similarity between the characteristics of a domestic novel, as defined by Baym, and Pride and Prejudice. Elizabeth is certainly not deprived of family and friends and thrust out into the world to forage for herself alone. It might be argued very loosely that she is, in a manner of speaking, cast out of the friendship of society because of her family's behavior and because of her father's inability to be frugal with his estate, which leaves her without a significant dowry, but this would be a weak argument indeed.
In some ways, Jane might be said to illustrate these characteristics in a limited sense in one or two situations--though not overall nor consistently--specifically (1) when her mother sends out into a coming rainstorm on horseback to Netherfield and (2) when she lies alone there in a fever and (3) when Miss Bingley and her sister reject Jane's society while they are all in London. This third one crushes Jane's spirit for a time while afterwards she exerts herself, relies upon her inner strength and resources and, in the end, what she sought (Bingley) comes to her unbidden in the style of a domestic novel. But again, this would be a weak argument indeed.
In short, it might reasonably be said that Pride and Prejudice demonstrates elements of Baym's definition of domestic novel in some segments of the novel and in one or two characters of the novel for momentary events or circumstances though it is not a domestic novel. Two other reasons an analysis of it as a domestic novel cannot stand up are that (1) Austen advocates following reason to find right and moral behavior and (2) she advocates reason over emotional feeling while using Lydia and Kitty as her primary lessons against ruling choices by feeling, as domestic novels advocate.