Does a woman have to cover her head while reading the Qur'aan as she does in salaah?
No it is not necessary... There's no evidence for it at all. For adab sake though, covering is good. But again, there's no evidence to show it is required. And Allaah knows best.
http://www.islamweb.net/emainpage/index.php?page=showfatwa&Option=FatwaId&Id=84572
