The girl was waiting in line at a food stall at the Handmade Parade event in Hebden Bridge on Sunday June 26 when a dog, believed to be a Staffordshire bull terrier, jumped up biting her face and leg.
The child has since had to have reconstructive surgery to an eyelid and has suffered potentially irreparable damage to her lower tear duct.
Officers want to speak to two men in connection with the incident who are both described as white, aged around 50-years-old, of quite broad build, wearing glasses.
One was also described as bald or with very short hair and wearing a black or navy and white horizontal striped shirt.
PCSO Gareth Helliwell, of Valley North Neighbourhood Policing Team, said: “Two men with the dog have apparently left the area without checking on the girl’s welfare or leaving any details. We need to identify these two men and would urge anyone with information about who they are, or indeed the men themselves, to come forward.”