Answered by Shaykh Faraz Rabbani
If one has not had sufficient sleep, such that one knows that she will be disturbed or ill during the day for not having slept more, is it permissible to sleep again after praying the fajr prayer?

Walaikum assalam,
It is not sinful to sleep after one performs the Fajr prayer.
It is disliked (but not sinful) to sleep after Fajr time enters, until one performs the Fajr prayer, [Haskafi, Durr] because:
a) this could lead to missing the Fajr prayer;
b) this is a time that it is recommended to spend in the remembrance of Allah.
Once one has performed the Fajr prayer, it is:
a) recommended to remain in the remembrance of Allah until Sunrisegreat reward has been mentioned in the Prophetic hadiths for this, including that its reward is akin to Hajj and Umra;
b) not disliked to sleep. [Ibn Abidin, Radd al-Muhtar]
And Allah alone gives success.
Wassalam,
Faraz Rabbani