Q: What religious knowledge in which is an obligation upon the women to acquire knowledge about?
A: The obligation upon her is to acquire knowledge about her ‘Aqeedah [i.e. Islamic belief] from the Qur’an and the Sunnah, afterwards acquire knowledge about the prayer—the manner in how the Prophet, sallahu alaihi wasallam, had prayed. When in the case she has wealth—she must acquire knowledge concerning what Allah has placed upon her [i.e. rulings] from the Zakât.
When in the case takes on the profession o selling and buying—she must acquire knowledge of the rulings (verdicts) of selling and buying; like this in whatever task she is to engage in—then it is becomes an obligation upon her to acquire knowledge of the verdicts in that task.
Thus by definition that is meaning of the hadith of the messenger of Allaah:
طلب العلم فريضة عل كل مسلم
“Seeking religious knowledge is an obligation upon every muslim.” [Hadith of ‘Anas bin Malik /authenticated by Shaykh al-Albani]
Like this in the case she is a doctor it is an obligation upon her to learn whether it is permissible for her to be alone with a man? Is it permissible for her to give medical treatments that are haram [i.e. containing alcohol etc.]?
It is incumbent to have awareness, from the Qur’an and Sunnah, of the job/task in which she is to engage in—I mean proofs and evidences from the Qur’an and Sunnah; I don’t mean that she should be restricted regarding the science of Tibb [i.e. medicine] over the knowledge of Qur’an and Sunnah.