Landmark legal proceedings have been launched against the Commonwealth Government over the alleged negligence of a five-year-old girl at Nauru detention centre.

Darwin lawyer John Lawrence on Friday told the Northern Territory Supreme Court the Iranian asylum seeker suffered significant mental injuries caused by a year spent in detention.

He said medical records showed she suffered post-traumatic stress disorder (PTSD), severe anxiety disorder, severe depression and bed wetting.

He said the girl's family wanted compensation from the Commonwealth for allegedly breaching its duty of care.

They are also seeking an injunction stopping their return to Nauru.

Lawyers representing the Commonwealth argued the case needed to be heard in the Federal Court as it involved a migration decision.

In April the ABC obtained medical records of the girl completed between January and February this year.

"This child should not be sent back to Nauru as she continues with a significant PTSD syndrome to the exposure to traumatic events during her previous stay, with ongoing severe anxiety symptoms, and risk of self-harm," one of the reports said.

It records the prescribing of anti-depressant medication to the girl.

The report said she was "still talking of hurting herself as per previous threats, parents are worried about when she is on her own at school, that she could hurt herself".

Another report said the child was wetting the bed and soiling herself during the day and at night, while a separate report said she displayed signs of anxiety that may have been getting worse.