"That is something that we are pleased to do because Canada is a country that understands how important it is to stand up for human rights, to stand up for women's rights around the world", Trudeau said, during a media availability in Regina.
Still Tamara Wood, a lecturer in forced migration at the University of New South Wales, said the speed with which her case is being treated appears quick, but "not unprecedented".
Ms Qunun's desperate tweets ricocheted across social media with the #SaveRahaf hashtag drawing an outpouring of support but also the bile of some hardliners in her native country.
Her case has drawn global attention to Saudi Arabia's strict social rules, including a requirement that women have the permission of a male "guardian" to travel, which rights groups say can trap women and girls as prisoners of abusive families.
She was stopped at a Bangkok airport last Saturday by Thai immigration police who denied her entry and seized her passport.
"Usually it's really very slow", said Mary Anne Kenny, a veteran legal practitioner and expert in Australian migration at Perth's Murdoch University.
She said she raised Australia's concerns about the case with Thailand's deputy prime minister and foreign minister.
Qunun had flown to Thailand from Kuwait to escape her family, saying she feared they would kill her because she renounced Islam.
On Monday evening, Thai authorities allowed her to enter the country.
West Ham tell Arnautovic to honour contract
Callum Wilson is believed to be their primary target, but it would likely take a huge offer to prise him away from Bournemouth. It remains to be seen whether Arsenal will bring in any new players this months during the January transfer window.
Rahaf Mohammed al-Qunun boarded a Korean Air flight from Bangkok to Seoul late on Friday night before catching a connecting flight to Canada, Thailand's immigration police chief Surachate Hakparn says.
The developments come after the teenager, who will be flying from Bangkok to Seoul before taking a connecting flight to Canada, was given refugee status by the United Nations high commissioner for refugees on Wednesday.
"Canada has always been unequivocal that we will always stand up for human rights and women's rights around the world", Trudeau said. She said she was fleeing abuse by her family.
The foreign minister there, Marise Payne, met with senior Thai officials in Bangkok on Thursday.
Footage released by Thai immigration shows Abdulilah al-Shouaibi, Saudi embassy charge d'affaires in Bangkok, complaining in a meeting Tuesday with Gen Surachate that Ms Qunun's smartphone should have been confiscated.
Alqunun deactivated her Twitter account on Friday.
In recent weeks Canada has issued sanctions against 17 Saudis linked to the killing of dissident journalist Jamal Khashoggi inside Saudi Arabia's consulate in Istanbul, Turkey and is reviewing its deal to supply light armoured vehicles to the kingdom.
'Rahaf received death threats and for this reason she closed her Twitter account, please save Rahaf life, ' @nourahfa313 wrote.