But the latter option brought its own dangers.
The videos and pictures of Bana documenting the Bashar al-Assad regime's destruction of the city that Fatemah had posted on Twitter - watched by millions - had made them instantly recognisable.
Bana had become an icon representing Syrian children living through the nightmare of siege and bombardment. Assad dismissed the account as propaganda.
"We had a special fear that was greater than that of other people - the soldiers would definitely snatch Bana if they saw her," Fatemah said, speaking from Turkey.
In their final weeks in east Aleppo the family had been forced to move from their home in the al-Shaar neighbourhood, after it was hit by an air strike which left her husband injured.
Then, as government troops closed in on the last remaining patch of rebel territory, they were having to move every few days from one abandoned house to another.
The truce and evacuation deal reached between the regime and the opposition on December 13 brought Fatemah little comfort.
"Those last moments in Aleppo were the worst," said Fatemah. Bana and the family spent three days out on the street waiting for government buses that were delayed by disagreements between the two sides.
Bana and her two younger brothers, Mohamed and Noor, were wrapped up in all the clothes they had to keep warm in the sub-zero temperatures. Fatemah and her husband Ghassan used what was left of their possessions to light a fire.
"We were waiting for a long time in the cold without food or clean water. We thought they would never come," said the 26-year-old English teacher. "We were so nervous and afraid - afraid we might die there waiting."
When the buses finally arrived, Fatemah made the difficult decision to send Bana on ahead with another family to avoid detection.
"I was very careful. Bana was put on another bus alone and I was hiding with other people," Fatemah told the Telegraph. "I hid behind a hijab, which I pulled over my face and looked down the whole time. I stayed in a big group of other women to try to be anonymous.
"I worried so much for Bana I thought the fear would kill me."
It was with mixed emotion that the family left Aleppo, the only city they had ever known. The regime's "surrender or starve" tactic had left east Aleppo flattened. They knew giving up Aleppo would be giving up the revolution, but they were quietly glad their children's suffering would end.
Bana's tweeting had attracted the attention of the Turkish government, a key backer of the opposition against Assad. So when they reached northern Syria, President Recep Tayyip Erdogan sent a special representative to meet them and have them airlifted out of the country.
"When we arrived (in Turkey) Bana shouted 'We are in heaven!' She did not remember that the world outside Aleppo was not bombed," Fatemah said.
The family was granted a private meeting with Erdogan, who posed for photos with Bana on his lap.
For the last two weeks, Fatemah, her husband Ghassan and three young children, have been getting used to their new life in Turkey, in a location the Telegraph is withholding to protect their safety.
"Bana loves her new surrounding because all she knew was destruction," Fatemah said. "Her brothers just enjoyed eating their first sweets and biscuits in months. They had no real food for a long time. Even I was excited about the food."
Bana is no longer having the nightmares that used to plague her every night and is planning to read the whole Harry Potter series, which were sent to her by the author JK Rowling to show her support.
The children are not yet enrolled in school, but hope to be once their asylum application is approved. She still has dreams of following her mother into teaching and hopes to do so someday back in Aleppo.
"Of course we want to move back, it will always be our home," Fatemah said, mournfully. "But I don't know when peace will come back to Syria.
"I really hope Assad and the opposition will reach an agreement someday. We don't care who's in power, even if it means Assad. We just need peace. Power doesn't matter, lives matter."
Originally published in the Telegraph UK