She was reportedly seen by a psychiatrist on the island last week who "recommended she be moved to Australia".
SBS News contacted the Department of Home Affairs with questions about the welfare of the girl but has not received a reply.
It comes only days after a 12-year-old Iranian refugee boy on Nauru was flown to Australia after refusing food for more than two weeks.
The cases have prompted refugee advocacy group to warn of dramatically deteriorating mental health among children in Nauru and speculation some may have resignation syndrome.
Founder and president of Doctors for Refugees Dr Barri Phatarfod told SBS News via email that "every single child [on Nauru] likely has some form of mental health issues".
"It's impossible not to when they are referred to only by number ... and there is no prospect of release," she said.
Dr Phatarfod said most, if not all, of the children had both witnessed and experienced extremely unsettling events.
"In Australia, we have government regulations as to what a child can even see on TV, so concerned are we about the effects of violence and distressing images on young minds," she said.
"Yet for the children on Nauru, many of whom have already witnessed unimaginable traumas, there are no such concerns."
Previously, Home Affairs has told SBS News that "a range of care, welfare and support arrangements are in place [on Nauru] to provide for the needs of refugee children and young people".
The offshore policy is designed to deter people embarking on treacherous sea journeys, but the United Nations and other rights groups have criticised the camps' conditions and long detention periods.
Readers seeking support and information about suicide prevention can contact Lifeline on 13 11 14, Suicide Call Back Service on 1300 659 467 and Kids Helpline on 1800 55 1800 (for young people aged 5 to 25).