Celia Carmichael is an imaginative eight-year-old in 1957 Box Hill, Australia, who is devastated by her grandmother's death. After the funeral, Celia envisions a monstrous blue hand of a Hobyah reaching into her bedroom window. When she screams, her mother, Pat Carmichael, comes to comfort her. Pat takes Celia to the backyard where the screeching is revealed to be a possum.
The following day, Celia meets her new next-door neighbors, Alice Tanner and Evan Tanner and their children, Meryl Tanner, Karl Tanner, and Steve Tanner. On Celia's birthday, she is disappointed to receive a bicycle instead of a pet rabbit; her father, Ray Carmichael, reassures her that rabbits are vermin. Later, at mass, the priest delivers a sermon deriding the Australian Peace Council as a communist front. Celia finds comfort in visions of her grandmother, especially when she is harassed at school by her cousin, Stephanie Burke. While Celia plays with the Tanners in a rock quarry one day, Stephanie Burke and her brothers steal a wooden Japanese mask belonging to Celia's grandmother, and they chase Celia.
Celia's father becomes angry when he discovers the Tanners are members of the Communist Party of Australia, which strains the two families. He forbids Celia from visiting the Tanner home and, to appease her, buys her a pet rabbit named Murgatroyd. When Celia is found speaking to the Tanner children again, he grounds her for a week and informs his brother, Inspector John Burke — the local sergeant and Stephanie's father — of the Tanners' beliefs. Celia experiences a disturbing nightmare in which her grandmother scratches at her window, followed by a gruesome Hobyah.
One night, Celia and the Tanner children sneak to the rock quarry, where they make effigies of Burke as well as Stephanie Burke and Ray Carmichael. In a ritual around a fire, the children stab the effigies with needles before throwing two of them into Stephanie Burke's bedroom window. Celia places the effigy of her father in a cupboard, and when he discovers it, he beats Celia with a belt. After Evan loses his job due to Ray's disclosure of his communist beliefs, Celia and the Tanner children return to the quarry and burn the effigy of Ray, wishing death upon him. They are ambushed by Stephanie and her friends, who lock them in a shack and injure Murgatroyd with a firepoker.
Celia and the Tanner children retaliate by throwing bags of flour onto Stephanie and her brothers during church mass. Later, the Tanners relocate to Sydney so Evan can find new work. Burke later arrives at the Carmichael home to confiscate Murgatroyd, as rabbits are deemed an invasive species and banned from being kept as pets. After several unsuccessful attempts, Burke finally takes Murgatroyd to the local zoo. Celia begins to hallucinate, imagining her uncle Burke as an evil Hobyah creature. At school, Celia defaces a newspaper photograph of Victorian premier Henry Bolte, turning him into a Hobyah.
After a series of petitions, the government eventually loosens the rule and allows individuals to keep pet rabbits with permits. Celia and numerous other families visit the zoo to reclaim their rabbits, but Celia and Heather Goldman find their rabbits dead. Later, Celia and Heather are left in Burke's care while Celia's parents go to play tennis. Celia again hallucinates, imagining Burke as a Hobyah, and shoots him to death with her father's shotgun. In a panic, the girls derange the house and throw Pat's jewelry into a stream, staging the scene to appear as a robbery-murder. They chain Burke's dog to a tree and stay by the quarry until Celia's parents return home to find Burke's body.
Celia's mother becomes suspicious when she notices Burke's dog and a bruise on Celia's chest shaped like the end of a shotgun. She chooses to hide these from the police and Celia's father. Later, Celia and Heather stage a mock execution for Burke's murder. Celia acts as judge, sentencing Heather to death by hanging, but it is revealed to be a prank. The line between fear and reality remains thin, and Celia's world is forever colored by the specter of the Hobyah and the harsh lens through which adults—politics, danger, and discipline—seem to view the world.
