Papers in respect of her challenge were submitted on May 30 last though no date has been set for the matter to come before the Court of Appeal.
Harrington (38) was last month convicted by a Central Criminal Court jury of beating to death Santina Cawley (2) on July 5 2019 at a Cork apartment complex.
Santina died from a traumatic brain injury and a severe spinal injury after suffering a fractured skull and fractures to her arm, leg and ribs while in the care of Karen Harrington.
The murder trial heard there wasn't a part of the little girl's body that wasn't bruised with a total of 53 injuries noted by the pathologist.
Doctors said the injuries suffered by the child were "unrecoverable."
She was handed a life sentence on May 16 after being convicted of Santina's murder by unanimous decision of the eleven-member jury following a harrowing four-week trial.
Harrington is now entering her second month of a life sentence imposed for the brutal murder of the little girl in July 2019 after she had been drinking and smoking cannabis for several hours.
Harrington had vehemently denied the murder - but was unable to explain how the toddler suffered such horrific injuries while she was alone with her in her apartment.
Extensive CCTV footage showed the only person who had entered and left the flat with Santina at the time involved was Karen Harrington.
It comes after Santina’s father, Michael Crawley, received a suspended ten month prison sentence for assaulting Harrington on a bus.
The 37-year-old was warned by Judge Olann Kelleher at Cork District Court that he was "a violent man" and could not be allowed to "take the law into your own hands."
The court heard that Cawley spotted Karen Harrington on a bus, boarded the bus, threw her to the ground and repeatedly kicked her.
The subsequent assault, which lasted between 10-15 seconds, was captured by the CCTV system on the bus.
Cawley then left the bus and rang gardaí a short time later to inform them what had happened and make himself available for interview.
Harrington was on bail awaiting her murder trial at that point.
Cawley of Leeside Apartments, Bachelors Quay, Cork pleaded guilty before Cork District Court to assault causing harm to Harrington early last year.
He was charged with assault causing harm to Karen Harrington at Merchant's Quay in Cork city centre on January 26 2021, some 18 months after his daughter's death.
Defence solicitor, Frank Buttimer, said his client was under tremendous strain at the time in January 2021 because of his daughter's murder, the repeatedly delayed court proceedings as well as other issues.
"He should not have done it - there may be some degree of understanding as to why he had some degree of a loss of composure," he said.
Mr Buttimer said the meeting on Merchant's Quay that day was entirely coincidental and resulted in Michael Cawley suffering a sudden loss of control and composure.
"He was enraged when he saw the person he believed, correctly as it transpired, that had killed his daughter."
Judge Kelleher said that, given all the circumstances involved, he would impose a suspended 10 month prison sentence.
"He will not get a second chance," the judge noted.
Mr Cawley had the ten month prison term suspended for two years once he entered a €400 bond to keep the peace.