Cookeroo bulwidarri was named by Butler et al. (2016). Its type specimen is QM F19798, a partial skull (partial adult skull, slightly warped, with left and right I1–3 alveoli, C1 alveoli, P3, and M1–4), and it is a 3D body fossil. Its type locality is White Hunter Site, which is in a Chattian terrestrial horizon in the Carl Creek Limestone Formation of Australia. It is the type species of Cookeroo.