At the moment they use Fastway Australia as the couriers and you are able to track Mailman parcels using Fastway Australia in AfterShip. This isn't officially acknowledged anywhere, it's just what I've figured out. It would be good to have the Fastway Australia entry copied and rebranded for Mailman.
"Mailman is a parcel delivery service with Australia’s lowest national flat rate prices, with no hidden fees or surcharges. We deliver from our store to any residential or business address in Australia (excludes PO Boxes, Locked or Private Mailbags, Parcel Lockers & Remote Islands). With free signature on delivery, track and trace, optional parcel protection and the convenience to print your own labels from home or office, with Mailman you can send parcels for less"