What does "wallaby" mean?

Wallaby: Any one of numerous species of kangaroos belonging to the genus Halmaturus, native of Australia and Tasmania, especially the smaller species, as the brush kangaroo (H. Bennettii) and the pademelon (H. thetidis). The wallabies chiefly inhabit the wooded district and bushy plains. [Written also wallabee, and whallabee.]