Her father, Sir Zulfiqar, belonged to a collateral branch of the ruling family of Malerkotla princely state in Punjab.

Qudsia was married in 1929, to Nawab Aijaz Rasul, the taluqdar (landowner) of Sandila in Hardoi district of what was then Oudh (now a part of Uttar Pradesh).

With the enactment of the Government of India Act 1935, the couple joined the Muslim League and entered electoral politics.

Begum Aijaz Rasul was instrumental in creating consensus amongst the Muslim leadership to voluntarily give up the demand for reserved seats for religious minorities.

During the discussions pertaining to the right of minorities in an assembly of the Drafting Committee, she opposed the idea of having 'separate electorates' for Muslims.

The Indian Women's Hockey Cup is named after her (Begum Rasul trophy)[further explanation needed].

She also took keen interest in literature and authored the book Three Weeks in Japan and contributed to various newspapers and magazines.