Chris Bowen says other countries struck deals for a billion doses of the Pfizer vaccine before Australia signed its agreement. Is he correct?

The claim

The first doses of Australia’s COVID-19 vaccination program have at last been administered, but concerns have been expressed that the rollout will be slowed by supply constraints.

In announcing Australia’s November deal with Pfizer to supply 10 million doses of its vaccine, Prime Minister Scott Morrison claimed the agreement, along with another deal signed with Novavax for 50 million doses, had put Australia at “the front of the queue”.

But, in January, the Opposition accused the Government of being slow to make deals, and that this would affect supply of the drug.

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“[B]y the time the Morrison Government did a deal with Pfizer, a billion doses had already been accounted for around the world. Australia wasn’t at the front…