I am starting to read Robert Irwin's book Night & Horses & The Desert: An Anthology of Classical Arabic Literature.
Here I list the Arabic authors mentioned in Chapter 1: Pagan Poets (A.D. 500-622). Bold ones are pagan poets that have substantial work cited in Chapter 1:
Ibn Qutayba (9th c. anthologist and literary critic)
Imru' al-Qays (Mu'allaqa)
Hammad al-Rawiyya (694-772) - rawis, anthologist and probably the first to make a selection of seven Mu'allaqat
'Antara Ibn Shaddad (author of one of the Mu'allaqat; poem cited a different qasida)
Al-Shanfara Al-Azdi (sa'alik poet; author of Lamiyyat)
Ta'abbata Sharran (author of Qit'a Nuniyya)
Al-Khansa' bint 'Amr ibn al-Sharid (woman poet of lament, 575-645?)
Khalaf ibn Hayyan al-Ahmar (733-96) possible rawi author of Lamiyyat
Chapter two is a discussion of how Qur'an is not considered literature in the tradition, and how it clearly has literary quality and have immense influence on subsequent Arabic literature.