She then entered directly into a doctoral program under the tutelage of Ezra Fleischer, in which she wrote her dissertation on the piyyutim of a paytan named Eleazar b. Qilar; she proved that this poet was a completely different individual from the famous poet Eleazar b. Qallir ("the Qalliri").

She later published this dissertation, including the full surviving corpus of Eleazar b. Qilar, as a book in 1988.

Elizur has been teaching at the Hebrew University for many years and has published nearly one hundred articles in the field of ancient and medieval piyyut for a scholarly audience.

In 1999, she wrote a book for a more general Hebrew-reading audience, A Poem for Every Parashah (שירה של פרשה), for which she won the prestigious Rabbi Kook Prize.

She has also published Sod Meshalshei Kodosh which traces the historical development of the Qedushta genre of Piyyut.