Ms Carbery, who was a chronic alcoholic, got so drunk on the day of the crash she "blacked out". She was banned from driving at the time because of a previous accident.
Faith was seriously injured and her sister Ava (6) and her friend Michaela Logan were killed.
Ms Carberry was later sentenced to six years imprisonment with two years suspended.
Faith sued her mother and her father Thomas Varden as owner of the vehicle.
Judgment has already been entered against the mother and the case against Mr Varden was later withdrawn and only remained against the Motor Insurer's Bureau of Ireland (MIBI), which was set up by the government and the insurance industry to compensate victims of accidents caused by uninsured drivers.
In the High Court yesterday, Mr Justice Peter Charleton approved a €200,000 settlement of Faith's case against the MIBI.
The judge said in terms of what happened to Faith, nothing can ever compensate her, but he hoped the tragedy in her life was now finished and she will do well.
Speaking directly to Faith, the judge said he was very sorry for everything she had been through, but he was sure she will have a great future.
Faith, of Clonguish Court, Newtownforbes, Co Longford, but who now lives in Tuam, Co Galway, had sued through her grandfather Anthony Carberry of St Mels Road, Longford.
As a result of the accident, Faith -- who had been sitting in the back seat of the car -- was removed to hospital after her spine had been stabilised at the scene.
She later underwent surgery and was transferred to Our Lady's Children's Hospital, Crumlin where she was treated in a spinal cast.
It was claimed Faith suffered severe psychological trauma and upset in circumstances where her sister had been killed in the accident.
Her counsel John Finlay told the court that it was a particularly sad accident and said Faith had a lot to deal with as her mother was jailed.
Faith now lives with her stepsister Marguerite Varden in Tuam where she is in sixth class at school.
Ruling the settlement, Mr Justice Charleton allowed the payment out of €2,000 to purchase a computer and printer for Faith.