Janet Hart raised proceedings at Airdrie Sheriff Court to exhume eight bodies at the Lanarkshire burial site in a bid to finally solve the 55-year-old mystery and lay her sister to rest.
Moira was just 11 years old when she disappeared in February 1957 after being sent on an errand to a local shop in Coatbridge, North Lanarkshire, by her grandmother.
No trace of the youngster was ever found and it has been widely accepted she was abducted, probably by a paedophile, and then murdered.
A number of years ago evidence emerged that suggested her remains may have been hidden in a grave in the town's Old Monkland Cemetery.
Moira's family has campaigned for a number of years for the site to be examined and Mrs Hart has now instructed lawyers to seek formal permission to dig up the site.
Speaking from her home in Australia, Mrs Hart said: "I really hope this brings the closure so denied to us.
"It's not too much to ask that my little sister, Moira, have her final resting place not in an unmarked grave, or in someone else's grave, but with her loving parents who grieved for their lost daughter daily, until they too were laid to rest."
The prime suspect for Moira's abduction and murder was paedophile Alexander Gartshore, who worked as a bus driver near the schoolgirl's home.
Gartshore, now deceased, was named as the killer in a deathbed confession by a fellow child abuser. His daughter Sandra Brown – who now runs the Moira Anderson Foundation which is backing the court bid – has investigated Moira's case for decades and has written a book stating that her father almost certainly murdered the schoolgirl.
She also said she believes Moira's body was somehow hidden beneath the coffin of a man, Sinclair Upton, who died a few weeks after she went missing. He is one of the bodies Mrs Hart is asking to exhume, along with Elizabeth Upton, who died in 1908, Joseph Thom, who died in 1923, Margaret Upton, who died in 1951, Elizabeth McNeilly, who died in 1976, Peter McNeilly, who died in 1978, Hugh Winterbottom, who died in 1985 and Mary Winterbottom who died in 1995.
Anyone with any objection to the exhumation can contact the court, however, it is understood that all of the families of the people buried in the lair have already given their backing for the work to be carried out.
A Strathclyde Police spokeswoman said:"If and when the authority has been given Strathclyde Police will need to ensure the appropriate forensic protocols are in place."