Health Minister Greg Hunt said Morrison was getting the shot to ensure Australians have confidence in the vaccine. An Australian Bureau of Statistics survey showed 76 per cent of men and 71 per cent of women want to get a vaccine jab.
Morrison's decision to put himself front and centre at the start is in marked contrast to New Zealand Prime Minister Jacinda Ardern's stated plan to wait until frontline border staff have theirs, because they are the "priority".
It spotlights their different approaches to their jobs and how they relate to the populations they lead.
Ardern is better at spotting the nuance and potential political trap, preferring in this case to stay out of the way to allow the focus to go on border staff most at risk of catching Covid-19.
Morrison's political persona is broad, bearish, blokey and sometimes a bit buffoonish. To him it feels right to make the running.
Morrison and Ardern have ridden waves of popularity over the pandemic. Australia's state leaders have drawn a collective tick as well. The crisis suited both leaders' skill sets, and the two countries have done an outstanding job in global terms.
Morrison filled the role of positive, reassurring, overall co-ordinator while states ran responses on the ground. An Australian columnist Shaun Carney wrote of Morrison: "He does not present himself as a leader of ideas or vision. He is about managing, keeping things as they are, getting through".
A Newspoll in the Australian released at the start of this week showed Morrison with a 64 per cent satisfaction rating. He dominates as preferred prime minister over Labor leader Anthony Albanese by 61 to 26 per cent.
That advantage could well hold through the vaccine rollout, economic recovery and reopening of travel.
However, Morrison's success last year with the pandemic cannot hide stumbles in other areas or erase memories of his bushfire debacle.
He is struggling to deal with a scandal which has engulfed parliament over the alleged rape of a ministerial staffer in April last year.
Home Affairs Minister Peter Dutton says police alerted him about the allegation on February 11. Morrison says he was not made aware of it until February 15. Other women have since come forward.
Labor's shadow minister for women, Tanya Plibersek, accused Morrison of "running a don't ask, don't tell government of cover-ups". Labor's leader in the Senate Penny Wong said "no matter what happens, he is never responsible".
Last night a bombshell broke with news of a historical rape accusation against a current cabinet minister.
Adding to a difficult week, Morrison lost his parliamentary majority with MP Craig Kelly becoming an independent. And a federal-run part of the vaccine rollout has already hit early turbulence.
It all follows a rare flare-up between Wellington and Canberra over a New Zealand-Australian woman arrested at the Syria-Turkey border.
Under Morrison, Australia has made some brash moves on the world stage, particularly on China and a boosted defence strategy. China's influence will only grow and realistic co-operation, where possible, is preferable to getting stuck in hardened positions.
The standoff with Facebook this week was a necessary push-back against big tech's rampant power, but the jury is out on how effective it will be.
It's worth remembering that the pandemic revived Morrison's political fortunes after his much-criticised handling of the devastating bushfires.
And that included a family trip from incinerated Australia to Hawaii - exactly the escape from ground zero move that Texas Senator Ted Cruz pulled while his state froze.
At times Morrison's confident, relateable style recalls another Texan, former president George W. Bush. Instead of Dubya, there's ScoMo. Instead of cowboy imagery there's bushman's shirts and league jerseys.
And despite the successful wrangling of Covid, there's also some of the Bush-style clumsy barging through minefields as they arise.
