Jane Austen certainly does address the theme of gender injustice to some extent in Pride and Prejudice through Charlotte Lucas's surprising marriage to Mr. Collins.
Austen makes it very evident that it is due to her situation that Charlotte forces herself to think of marrying Mr. Collins as an acceptable thing to do. The major problem with her situation is that, although her father was given a title due to his work as a mayor, Austen makes it very clear that Sir Lucas quit his trade business, bought an estate, and took on the leisurely life of a gentleman far too soon (Ch. 5). The result is that he has very little fortune to pass down to his children, and even his children must take on household chores. It is due to lack of fortune that Charlotte absolutely must marry. In addition, her choices for marriage are very limited as she has always been very plain. As Austen phrases it:
[For Charlotte], without thinking highly either of men or of matrimony, marriage had always been her object; it was the only honourable provision for well-educated young women of small fortune, and however uncertain of giving happiness, must be their pleasantest preservation from want. (Ch. 22)
Had Charlotte, like a man, been able to acquire an occupation, she would not need to make sure she was cared for through marriage. Hence, Charlotte's marriage to a ridiculous man due to necessity certainly helps portray the theme of gender injustice.