The 34-year-old — who can’t be named under a court order to protect the identities of two other children —- appeared in court Friday after pleading guilty to manslaughter in the October 2010 incident.
Lawyer Lisa Labossiere told court Friday her client was in desperate need of help after having her three children returned to her care about a year before her daughter's death.
Court heard the woman suffers from fetal alcohol syndrome and has a history of drug abuse and working in the sex trade.
The Crown is seeking a 12-year prison term, while the defence has asked for eight years behind bars.
Provincial court Judge Sid Lerner said he would deliver a sentence on April 10.
The little girl died in hospital of major injuries suffered from repeated assaults while living in a small community about 90 kilometres southeast of Winnipeg.
Crown attorney Breta Passler said the woman initially said her daughter had fallen and injured herself. She later admitted that she beat the girl on multiple occasions.
Labossiere said the provincial child welfare agency failed to follow through on suggested therapy and home respite which her client needed to properly care for her children.
"She was feeling extremely overwhelmed. (The accused) doesn’t have all the tools in the toolbox that you or I may have in terms of parenting," said Labossiere.
"Child and Family Services does have a degree of responsibility."