Answer
Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Driving, for men and women, is generally permissible as long as one is capable to and has the driving license.
Answering your question about women’s right to drive, Dr. Wael Shehab, PhD in Islamic Studies from Al-Azhar University and currently the Imam of the Downtown Toronto Masjid in Canada, states:
There are no impermissible deeds in Islam except those which are prohibited by clear proofs either in the Quran or the Sunnah, or the ones that violate or contradict the rules and teachings of Shari`ah.
Generally speaking, women have the right to drive as long as they are capable to and have the drive license.
I know that in some countries a woman is not permitted to drive, but this administrative rule might be based on some particular or local considerations which don’t affect the basic permission and legality in other countries of the world.
Given the above, both men and women are basically allowed to drive once they get the legal driving license.
Drivers, men or women, should pay due attention to traffic and driving rules. They should not expose their or other people’s lives, health, or properties to danger.
Allah Almighty knows best.