All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Da‘wah is the mission of all messengers and prophets. Allaah The Almighty Says (what means): {O Prophet, indeed We have sent you as a witness and a bringer of good tidings and a warner. And one who invites to Allaah, by His permission, and an illuminating lamp.} [Quran 33:45-46]
Furthermore, Da‘wah is the way adopted by the Prophet, sallallaahu ‘alayhi wa sallam, and those who follow his Sunnah, for Allaah The Exalted Says (what means): {Say, "This is my way; I invite to Allaah with insight, I and those who follow me. And exalted is Allaah; and I am not of those who associate others with Him."} [Quran 12:108]
Additionally, the Prophet, sallallaahu ‘alayhi wa sallam, ordered all the believers to shoulder the responsibility of calling people to the truth, even if it is by reporting a single verse on his authority. [Al-Bukhari]
This prophetic command addresses both men and women, and the qualifications required in a female Daa‘iyah are the same as those required in the male. There are many examples in the Islamic history of women who undertook the responsibility of Da‘wah, and were known for their comprehensive understanding of religion and adherence to the truth, like ‘Aa’ishah, Umm Salamah and Umm Ad-Dardaa’ .
For further information, you may read Fatwa 85658.
Allaah Knows best.