Celine is the daughter of Peter Moody, who trained the racehorse Black Caviar. She has a twin sister, Breann Moody, who plays in the AFLW for Carlton. Both attended St Margaret’s School, where they played football together. Throughout her junior career Moody usually played as a defender. She trained as an information systems technician for the Australian Army and took a four-year break from football. On her return in 2018, Moody joined Carlton’s VFL Women’s side. She played 12 games, mostly as a forward and ruckwoman, wearing number 36.
Having not played football for the previous three years, Moody was eligible to join an AFLW club during the 2018 off-season as a rookie signing. She was recruited by the Western Bulldogs as their second signing and debuted in the opening round of the 2019 AFLW season in a victory over Adelaide at Norwood Oval. It was revealed that Moody had signed a contract extension with the club on 16 June 2021, after playing every game possible for the club that season.
- Statistics are correct to the end of the 2021 season.