Broagan McCuaig faces an eight-week hospital stay for further surgery to help her recover from the injuries.
She was playing with friends on Friday when she was mauled by two American bulldogs in Gartloch Road, Garthamlock.
She suffered serious bite wounds to the face and a shattered leg, and has needed dozens of stitches and a skin graft.
Broagan is currently being treated in the high dependency unit at Yorkhill Hospital, in Glasgow, where she has undergone two major operations and faces further treatment, including skin and muscle grafts to her legs.
Yesterday, her parents Tracy Cox and Neil McCuaig, who have five children, hit out at the dogs’ owners.
Ms Cox said: “I am angry. I am really angry. Nobody should have these dogs. They are for farms and people with fields. They are to bring down bears or cattle, not for a wee block of flats.
“You should have to have a licence to have a dog and have a good reason for needing one. I think everyone should only have one pet.”
Ms Cox said her daughter was “terrified” by the thought of returning to the flats were she was attacked.
She added that she “froze” with horror after hearing Broagan’s screams and ran outside to see the two dogs savaging her daughter.
Ms Cox said: “It was the worst day of my life. It was horrible.
“Just to think she was inside one minute then outside screaming the next, just screaming, ‘Help me, help me’. That’s all I can remember.
“She is doing okay now. She is talking now, she is speaking. She was just being cheeky to me there so she is coming back. She is so brave. I just want my little girl back.”
Broagan is now sitting up in bed and chatting with her family. But Ms Cox said she had been left traumatised.
“It has had a terrifying impact,” she said. “She is wanting to go home but she is getting flashbacks of what happened.
“I think it’s all coming back to her now, and she is getting frightened.
“She does not want to go back to that house. She doesn’t want to leave her friends but she doesn’t want to go back to that close. She will never be allowed out the back to play again.
“She keeps saying, ‘Are the dogs away? The dogs away? Are they there? Are they there?’ She thinks they’re still in the house down the stairs from her, and we’re just reassuring her that there’s nothing there anymore and that they’ve been taken away by the police.”
Ms Cox added: “I don’t know how it started. Broagan was round the back playing and the next minute there was screaming and banging at the door.
“I could see these two big animals were pulling at her.
“There was a man trying to get her. I blanked out, I just froze.
“I knew it was going to be bad.
“She was in shock. She was asking, ‘Am I going to be all right?’ ”
Mr McCuaig, 39, had been walking his own dog when the attack happened.
He said: “She is lucky to have survived.
“If it had not been for the boys who helped her, she might not be here now.”
The flat where the dogs’ owners lived was boarded up yesterday, and neighbours said that the couple had moved out.
Broagan has still not seen the extent of the injuries to her face, but has been able to feel the swelling.
Ms Cox said: “She has not seen herself yet.
“She said, ‘I look stupid’ and I said ‘no, you’re beautiful. It’s only because you can feel it’s swollen.’ The nurse said she was absolutely gorgeous and so brave.”
A Police Scotland spokeswoman said last night: “A man aged 34 and a woman aged 33 are subject of a report to the Procurator Fiscal.”