Until recently every past prime minister was offered a Companion in the Order of Australia, the Order's highest honour.

Paul Keating famously refused it - reports from the time are summarised in Wikipedia here:

Retirement and later life[edit]

 In 1997, Keating declined appointment as a Companion of the Order of Australia, an honour which has been offered to all former Prime Ministers since the modern Australian Honours System was introduced in 1975.^[41]

The footnote takes us here 

http://primeministers.naa.gov.au/primeministers/keating/after-office.aspx

The NAA publication is a fair bit out of date - Kevin Rudd became a former PM in June 2010 (and again in 2013).    Gillard was rolled on 26 June 2013.   That's five years to mull over Rudd's first period of achievement as PM and 2 years for analysis post Gillard's possie.

I remember the hooha when Mr Keating knocked back the gong.   There appeared at the time to be some sort of convention that those who'd held Australia's top job should get the top honour.

John Howard was made a Companion in the Order in August 2008, 9 months after his November 2007 election loss.

Bob Hawke was made an AC in 1979 before he became Prime Minister.

The late Gough Whitlam was made a Companion of the Order of Australia in June 1978 on leaving the Parliament.

The late Malcolm Fraser was made a Companion in 1988.

The entire list of Companions is at the link below, replete with many state premiers as well as the former PMs.

https://www.itsanhonour.gov.au/honours/awards/medals/companion_order_australia.cfm#recipients

Rudd and Gillard are notably absent.  I can't imagine either of them doing a Keating and knocking it back.  Each of them would have the draft citation in their back pocket - Rudd for services to the world and Gillard for calling out misogyny or something new agey.

Five years now to analyse Rudd's "outcomes"  first time round in the top job.   Two years post Gillard.   And still no blue ribbon to recognise their "achievements".

Like to take a stab at what would be in their nomination material?