There isn’t a lot of information, but they have a post office!
Australia Post provides reliable and affordable postal, retail, financial and travel services. You’ll find the Australia Post Office Shop next to Airport Guardian Pharmacy at International Terminal (T1) before Customs. Its open 6am- 8pm daily. (source)
I imagine there are drop boxes in the domestic terminals (T2 and T3), but I can’t find any usable maps after 30 minutes of looking around their site. If anyone has experience, let me know and I’ll update this page.
Last updated 10 June 2017