Like Heathrow Harry, we have never had to show any paperwork on entry to Australia. However, we have always had a paper copy of the visa Grant letter with us just in case.
I'm not sure about being denied boarding a flight to Australia if one does not have a visa (my son in Sydney says people turn up without visas from time to time and are put on the next flight home).
However, I believe visas are checked at check-in when travelling to the USA.
I will ask the question at the Qantas desk on Wednesday and see what they say.