According to First on TV News in Australia, the boy was playing with his sibling when he allegedly fell on the staircase.
The parents reportedly told the police that they gave the boy a painkiller and then put him to sleep but called an ambulance later when his condition got worse.
Detectives were at the scene gathering evidence to ascertain what led to the death of the little boy.
The couple was arrested and taken for questioning awaiting post-mortem results.
Authorities in Australia were yet to comment on the matter that was already in the hands of police.