All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, we would like to thank you for your good intention, and we ask Allah to reward you generously and help you accomplish your objective. Verily, Allah is near, and He answers the supplications of those who call upon Him. So supplicate Him and ask Him for what you want; Allah, The Exalted, says (what means): {And when My servants ask you (O Muhammad) concerning Me - indeed I am near. I respond to the invocation of the supplicant when he calls upon Me. So let them respond to Me (by obedience) and believe in Me that they may be (rightly) guided.} [Quran 2:186] There is also no doubt that calling people to Allah is one of the greatest good deeds that draw one closer to Allah, and He commanded us to perform Da‘wah (proselytization) and informed us of the great rewards that it yields and the fact that it is a means of deliverance and success. Allah, The Exalted, says (what means): {And let there be (arising) from you a nation inviting to (all that is) good, enjoining what is right and forbidding what is wrong, and those will be the successful.} [Quran 3:104]
The Prophet, sallallahu ‘alayhi wa sallam, encouraged Muslims to carry out Da‘wah and underlined its merits in the Sunnah. Sahl ibn Sa‘d, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, said to ‘Ali, may Allah be pleased with him, when he, sallallahu ‘alayhi wa sallam, sent him to Khaybar, “...invite them to Islam and inform them of their duties towards Allah in Islam; for, by Allah, if one man is guided through you, it would be better for you than having red camels (the most precious camels).” [Al-Bukhaari and Muslim]
Abu Hurayrah, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, said, “The one who called (people) to righteousness will get the same reward as those who followed him, without their rewards being diminished in any respect....” [Muslim]
May Allah reward your husband generously for doing his duty of providing for his family. Although the husband is not obliged to provide what is beyond the obligatory spending for his wife, he should not withhold from offering her whatever she needs, and he should support her in carrying out good deeds.
As for your question as to whether you should work or not, if you are asking about the obligation to work, then you should know that you are not obliged to work to earn the money needed for practicing Da‘wah. If you are asking about the permissibility to work, then know that it is permissible for you to work; however, you have to get your husband's permission to do that.
It would be good if you could study in an academic institution and earn a degree in Islamic studies because this would qualify you to work in the educational institutions that require an academic degree. However, you should know that seeking religious knowledge and calling people to Allah (Da‘wah) are not conditional upon earning a degree or formal studying. There are many ways to acquire religious knowledge, especially through the internet. There are plenty of online Islamic lectures and lessons delivered by a large number of reliable scholars of whose knowledge you can avail yourself.
There are endless means to practice Da‘wah and invite people to Allah; there are many social outlets to call people to Allah, such as doing that within families or neighborhoods, or at Quran-teaching centers and the like. On the other hand, Da‘wah does not require acquiring great Islamic knowledge; if a Muslim learned one verse or hadeeth and fully understood it, he can teach it to his fellow Muslims without exerting too much effort to learn what he does not know. ‘Abdullah ibn ‘Amr, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, said, “Convey (my teachings) to the people, even if it were a single verse.” [Al-Bukhaari] Al-Haafith Ibn Hajar quoted Al-Mu‘aafa An-Nahrawaani in his book Al-Jalees, “He said, 'even if it is one verse,' so that everyone who heard him would hasten to convey whatever they heard of the verses, even if it were very little, so that in this manner everything that he, sallallahu ‘alayhi wa sallam, brought would be conveyed.” [Fat-h Al-Baari]
Allah knows best.