Reference: http://mufti.af.org.sa/ar/content/حكم-سجود-التلاوة-للمرأة-الكاشفة-عن-رأسها
Question: A woman reads the Qur.aan with her head uncovered, and when she comes across an aayah wherein there is a prostration [to be made], should she do the prostration with her head uncovered, or should she cover it [and then do the prostration]?
Response: As for her reading the Qur.aan with her head uncovered, then there is no harm [in her doing so]. That is because the covering of the head is for the prayer, as He ﷺ said:
As for the prostration of recitation, then whoever from the scholars is of the opinion that the prostration of recitation is a prayer, then she must cover her head when she wants to do the prostration. And whoever [from the scholars] is of the opinion that [the prostration of recitation] is not a prayer, then she is not required to cover her head. [That said] however, it is safer for her to cover her head when she wants to do the prostration [of recitation] – just so she removes herself from any disagreement in this [matter].