She said she was aiming for Australia where officials had said they would give serious consideration to her claim for asylum, which was endorsed as legitimate by the UNHCR on Thursday.
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".
The case has highlighted the cause of women's rights in Saudi Arabia.
Ms. Payne's visit has also thrown a spotlight on another refugee case, involving Bahrain footballer Hakeem al-Araibi, who has refugee status in Australia but was arrested at Bangkok airport a year ago after arriving for his honeymoon.
Alqunun had previously said on Twitter that she wishes to seek refuge in Australia.
Ms.al-Qunun's case was dealt with on a fast-track "emergency" basis in light of the urgency of her situation.
The 18-year-old has said she was fleeing from her family out of fear they would kill her for renouncing Islam, something that is punishable by death in Saudi Arabia.
But al-Qunun's savvy use of Twitter throughout her ordeal at Bangkok airport, including tweeting videos of her barricading herself in a hotel room, galvanised a global campaign and calls for her to be granted asylum. "I do note that there are legal proceedings underway in relation to Mr.al-Araibi, and Australia will continue to be in very close contact with Thai authorities in relation to this".
Earlier a Thai immigration official told news agency Reuters that the 18-year-old would be heading to Canada on Friday (January 11) evening.
Her father and brother arrived in Bangkok on Tuesday, but Ms Qunun "refused to see" them, according to Thai Immigration Chief Lt Gen Surachate Hakparn, who has been caught up in the worldwide firestorm since Ms Qunun's arrival.
Immigration chief Surachate Hakparn said al-Qunun's father and brother, who have arrived in Thailand, could not object to the United Nations process as she has already been granted refugee status.
By Friday, Alqunun had closed down her Twitter account.
She was then allowed to enter Thailand and processed as a refugee.
"Canada has always been unequivocal that we will always stand up for human rights and women's rights around the world", Trudeau said. Her friends said she had suffered abuse at their hands.
The office of Canada's foreign minister however, said it could not confirm that asylum had been granted.
Last year Saudi women took to social media wearing their abayas - a loose, all-covering robe worn in public - inside out in 2018 to protest the dress code, which is strictly enforced by police.
Qunun's Twitter account was no longer active on Friday.
Rahaf Mohammed Alqunun's appeal for refugee status has underscored the severe restrictions that women in Saudi Arabia face.
"I understand that there have been death threats against her but I don't know the details", said Phil Robertson from Human Rights Watch, adding even threats from online trolls need to be taken seriously.