Eman al-Obeidi was heading from the rebel-held city of Benghazi to Washington DC, her sister Marwa said.
Eman al-Obeidi's case came to attention when she rushed into Tripoli's Rixos Hotel in March and told her story to foreign journalists staying there.
Earlier this week, Ms Obeidi was deported from Qatar.
She had sought refuge there after arriving from Libya, via Tunisia.
Dispute in Qatar
In Benghazi, Ms Obeidi's home city, Marwa al-Obeidi said a human rights group helped by US Secretary of State Hillary Clinton had organised for Eman and their father to travel in a private plane to Washington, via Malta and Austria.
"We just want a chance for her to be treated psychologically and to rest," she told the Associated Press news agency. "My sister has just been through so much."
She also said Qatari authorities had been friendly to her sister until a few hours before she was made to leave.
"Eman wanted to travel directly to America from Qatar, but for some logistical reasons, Qatar wouldn't allow it."
As Ms Obeidi recounted her story to reporters in in March, government minders grabbed her and dragged her away.
She vanished for several days before turning up in Tunisia.
Ms Obeidi said she had escaped with the help of defecting military officers.