Footage has emerged that appears to show authorities holding a baby found abandoned at Doha's international airport.
The discovery of the infant led to a number of women, including 13 Australians, being forced to undergo internal medical examinations earlier this month.
Prime Minister Scott Morrison has described the strip searches as unacceptable and appalling.
But Labor has accused the government of being too slow to respond.
Labor senator Penny Wong said Foreign Minister Marise Payne should have stepped in sooner.
"To rely on bureaucrats, to rely on officials, as efficient as they may be, really demonstrates an absence of leadership from both the foreign minister and the prime minister," Senator Wong said on Thursday.
"I think these women deserve people to be held accountable. They deserve transparency, but they also deserve a government that's going to go into bat for them."
Home Affairs Minister Peter Dutton has defended Senator Payne's handling of the situation.
"I have never seen somebody more committed to what is in our country's best interests, in particular the protection of women, both here and abroad," he told reporters in Canberra.
"She will work, in many of these cases, behind the scenes not in the public light.
"I have found that Marise has achieved incredible outcomes for our country as a result of that."
The Qatari government has announced an investigation and expressed its regret.
Aviation workers are threatening to take action against Qatar Airways if the investigation is not transparent and comprehensive.
Work bans against Qatar Airways would be hugely significantly and highly disruptive.
The airline flew 27 per cent of all passengers in and out of Australia in July, maintaining a strong commitment to the Australian market as other airlines pulled out due to the pandemic.
The federal government is trying to find ways to return 34,000 Australians home.
Richard Olsen, NSW state secretary of the Transport Workers Union, said the strip searches were a brutal violation of human rights against the female passengers.
Mr Olsen said while Labor and Liberal figures had spoken in support of the women, it was clear action was only taken because of media reporting.
"The Australian federal government and the Qatari government have failed in their duty of care to all Australians who were on board the Qatar Airways flights," Mr Olsen said.
"Transport workers have expressed strong feelings about the issue and the abhorrence on the violations involved.
"TWU members have previously taken action against the government-owned Qatar Airways on human rights violations, which include gender discrimination and homophobia against workers, and they stand ready to take action against this airline."
The Qatari government said it was committed to ensuring the safety, security and comfort of all travellers and regretted the distress.
It said the baby girl was under medical care in Doha and the aim of the search was to stop the mother from escaping.
Five women of other nationalities were also strip-searched after being dragged off planes.
Australian Associated Press