The short answer is no.
The Governor-General has the power to dismiss ministers (including the Prime Minister) if they are unable to govern.
The Governer-General cannot (or never has) dismissed the elected Prime Minister and their party because people are now angry at how they are leading.
So what is the difference between now and the constitutional crisis of 1975?
Essentially, in 1975 Gough Whitlam and his Labor party were the elected leaders of Australia.
However, while Gough Whitlam won another election in 1974, his party did not have a majority of the Senate.
Because Whitlam did not have a majority in the Senate, the Liberal Party could use their control of the Senate and block any and all bills from passing through.
The Liberal Party then stated they would continue to block bills in the Senate until Whitlam (who was unpopular with the Australian public) called an election in House of Representatives.
In a nutshell...
This is obviously a complex issue but here are the major points:
Gough Whitlam refused to call the election demanded by the Liberal Party.
However, his party was unable to govern Australia because the Senate was at a deadlock, meaning no new bills were getting passed. The government was at a standstill.
This led to Governer-General Sir John Kerr dismissing Whitlam on the grounds that he could not govern Australia in the current state.
This is not the case with Scott Morrison.
It would be extremely unlikely that a Prime Minister would get dismissed because of how they are leading the country.
After all, why would Scott Morrison now divert from his stance on climate change and his policies on coal mining that so won him the election?
This is who we elected to lead, and his party is able to pass bills and govern based on the promises that won them the miracle election.
Whether or not this crisis should shift both the Labor Party and the Liberal Party's controversially conservative climate policy is another argument altogether, but according to public opinion, the answer seems to be a resounding, yes.
