Thomson's landlord alerted the department when she inspected the property - which was home to two of Thompson's other children and a menagerie of dogs, cats, ducks, rabbits and chickens - and saw her rocking back and forth, surrounded by animal faeces.
After she was arrested, Thompson told police she was relieved when Destiny died, didn't know what had happened to her body, and didn't care.
It took several hours for her to admit the baby "might" be in the shed, where the infant's body was found, partly mummified.
Prosecutor Carmel Barbagallo said during a sentencing hearing last week that Destiny had a broken rib but her body was so badly decomposed the official cause of death could not be ascertained.
"The offender was grossly reckless in her care and monitoring of the needs of the baby," Barbagallo said.
Defence counsel Helen Prince said Thompson had an underlying borderline personality disorder and as her depression worsened, she was "using meth so she could carry out the functions of daily living".