Her mother described the attack as "the worst moment of her life". The dog's owners were unavailable for comment.
A police spokesman said the Dangerous Dogs Act 1991 gave them no powers to take any further action.
Icy's parents, who released a photo of their daughter's injuries, said it was "disgusting" that police could not order the West Highland White Terrier be destroyed.
Her mother Jessica Thomas-Day said: "Dogs have more rights than humans. The law needs changing. I would not be allowed to attack anyone in my back garden yet a dog can."
She said their neighbours Wendy and Simon Butler, who have a holiday home in Portesham, but live in Salisbury, Wiltshire, had told officers that they were not prepared to have their dog put down.
'Snarling and screaming' The attack happened after Icy and her parents were invited to celebrate the dog's third birthday at the couple's Dorset holiday home on 24 July.
Mrs Thomas-Day said: "The dog leapt over Icy's hand holding the treat and the dog's face was in Icy's face and it scratched her a dozen times as well.
"The dog was making the most horrific noise like snarling and screaming.
"Icy was screaming as well and had her hands over her face which was covered in blood. I was hysterical."
Icy was taken by ambulance to Dorset County Hospital and her father Paul then drove her to Poole Hospital where she spent two-and-a-half hours in theatre having stitches.
She will return to hospital in two weeks to see if the eye has been damaged.
Mrs Thomas-Day said her daughter had permanently lost half of her eyelid and lashes on her upper left eye.
'Unfortunate incident' "She has beautiful, big, blue eyes but instead of people saying how beautiful her eyes are now they'll be asking what happened to her eye."
A police spokesman said: "In this incident, the Dangerous Dogs Act does not give the police powers to take any further action.
"This is because the attack took place on private property that belonged to the dog's owner.
"We have advised the family they may wish to consider civil action."
The spokesman said police would have been able to take action if the attack had taken place on public property, or private property that did not belong to the owner.
"It's a very unfortunate incident and our thoughts go out to the family but the police can only work with the legislation - they don't make the law," he added.