Does Australia have a parliamentary line of succession to the Prime Minister and if so, what is the order?
Yes, there are procedures in place to make sure the role of Prime Minister is always filled.
If the Prime Minister was unable to undertake their role for a short time, for example due to illness, the Deputy Prime Minister would become Acting Prime Minister. When the Prime Minister returns to duty, the Acting Prime Minister returns to their normal position of Deputy Prime Minister.
The Deputy Prime Minister also takes on the role of Acting Prime Minister when the Prime Minister is overseas or on leave. If both the Prime Minister and Deputy Prime Minister are unavailable, a senior member of the government can be temporarily appointed to the position.
If the Prime Minister died, the Governor-General would appoint the Deputy Prime Minister as Prime Minister. The government may then vote for another member to become their leader. If so, the newly commissioned Prime Minister would then advise the Governor-General to commission this member as Prime Minister, and resign.
An example of what could happen occurred in 1967. Prime Minister Harold Holt disappeared at sea and there was no one with the constitutional authority to advise the Governor-General as to what he should do. Using his reserve powers he terminated Mr Holt’s position as Prime Minister. He then appointed the Deputy Prime Minister, John McEwen, as Prime Minister. Three weeks later, when Mr Holt’s body still had not been found, the government chose John Gorton as their new leader. Mr McEwen then advised the Governor-General to commission Mr Gorton as Prime Minister and resigned as Prime Minister himself.
Prime Minister Anthony Albanese giving a press conference.

DPS Auspic
Description
Prime Minister Anthony Albanese giving a press conference at Australian Parliament House. Behind him are the Australian flag, the Aboriginal flag and the Torres Strait Islander flag.
Permission should be sought from DPS AUSPIC for third-party or commercial uses of this image. To contact DPS AUSPIC email: auspic@aph.gov.au or phone: 02 6277 3342.