A starting place for the answer to this question is a Wikipedia article, Veritable Records of the Joseon Dynasty.
Several aspects of the role and rules relating to historians in the series correspond to information in this article.
So far I have had no luck on the internet finding mention of female historiographers working during the Joseon dynasty. Is this aspact of the screenplay creative license?
What is the plot of Rookie Historian Goo Hae-Ryung?
Set in 19th-century Korea, a female historian faces gender discrimination but perseveres. She gets entangled with Prince Lee Rim, blurring lines between duty and personal involvement.
