A red Citroen Xsara was travelling northbound at junction 32, at Thurcroft, when police believe the driver lost control of the car, travelled onto the hard shoulder and then rebounded back.
At the same time, a blue Ford Fusion is believed to have collided with the Xsara.
A dog travelling in the Ford Fusion was thrown from the vehicle onto the carriageway and hit by a silver VW Golf and died.
The driver of the Citroen Xsara, a 25-year-old woman from Rotherham, sustained serious head injuries and a fracture to the leg.
The driver of the Fusion a 39-year-old man and the passenger a 37-year-old man, both from Leeds, sustained whiplash, chest and facial injuries.
The accident happened around 10.30pm on Saturday 14th July.
Anyone who may have witnessed the incident or has any information, is asked to contact the police on 101, or Crimestoppers on 0800 555111, quoting incident number 1377 of 14/07/2012.