"Labor has been supportive of the government's moves to consider humanitarian settlement in Australia given she has been found to be owed protection", Wong said.
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She then started a social media campaign, live-tweeting her case and attracting worldwide attention.
Qunun alleges abuse by her family - who deny the allegations - and rights groups also said she had renounced Islam, risking prosecution in conservative Saudi Arabia.
The young woman's story made global headlines after she was stopped at a Bangkok airport on Saturday by Thai immigration police, denied entry and had her passport seized.
Australia has dropped the strongest hints so far after the United Nations urged the country to accept her but its foreign minister said this week that it was still assessing the request.
She was later allowed to enter Bangkok on Monday evening by the Thai authorities after a tense 48 hours that saw her refuse to board a flight to Saudi Arabia and barricade herself inside a transit lounge hotel room, while the world watched the drama unfold on social media.
In a video clip of the meeting released by Thai immigration police, Alsheaiby is heard telling Thai officials: "From the moment she arrived, she opened a new account and her followers reached nearly 45,000 in a day. and I would have preferred it better if her phone was taken instead of her passport".
Payne told reporters that Canberra was "engaged in the steps of the assessment process of al-Qunun as required".
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Qunun had previously expressed wanting to come to Canada on her Twitter account, which was deleted on Friday after getting death threats, Reuters reported.
Thai authorities eventually allowed her to enter the country on Monday evening and the United Nations refugee agency referred Rahaf to Australia for consideration for refugee resettlement.
"She's just been receiving a lot of death threats", McNeill wrote, adding that Alqunun would be back on Twitter after a "short break".
Thai authorities had initially threatened to deport her after she arrived in Bangkok from Kuwait last weekend.
Rahaf Mohammed al-Qunun began tweeting from Bangkok's airport, and a campaign sprang up on Twitter prompting the Thai government to reverse a decision to force the young woman to go back to her family.
Mr Hakparn said Canada had also offered Ms Alqunun asylum and they were waiting for her decision.
'They don't know about my life and they don't know how my family treats me, ' she said.
Australia's foreign affairs minister, Marise Payne, is in Thailand on Thursday for an official visit.
If Canada is taking Alqunun, it could further upset Saudi-Canada relations.
Around midday on Friday, Qunun posted on her Twitter account that she had "bad and good news!"
The next day, Canada's Foreign Ministry issued a tweet calling on Saudi Arabia to "immediately release" Samar Badawi as well as "all other peaceful #humanrights activists".