Almost 20 years after Kathleen Mary O'Shea disappeared, a $500,000 reward is now on offer following Ms Parmenter's "relentless" efforts.
"I'm thinking of giving her a job in my office. She would make a great detective," Detective Senior Sergeant Brett Devine said of Ms Parmenter.
In 2005, Ms O'Shea, 44, travelled from Melbourne for the birth of her first grandchild in far north Queensland.
But she was a no show at her granddaughter's January 9 delivery.
Ms O'Shea was last seen on December 29, 2005 at Atherton near Cairns.
She was reported missing by family on January 13, 2006.
Her son Alan is one of two persons of interest, police said.
Det Devine has been the case officer for the past 18 years.
He said Ms Parmenter had been in constant contact seeking updates and coming up with theories.
"She's been quite relentless over the years. I don't know how many telephone conversations I have had with Lily over the last 18 years," he told reporters in Cairns.
"I think her mother would be very proud of her."
Ms Parmenter hoped to get some closure after police on Monday announced the hefty reward for information that leads to a conviction in relation to her mum's suspected murder.
"I have spent probably half of my life looking for mum and trying to find answers for mum," she said.
"I was a teenager when all this happened and I am now 37.
"To be able to get some closure now, it would give me a little bit of my life back."
Ms O'Shea was visiting her son Alan at Ravenshoe for her grandchild's birth in 2005, police said.
It is alleged she was dropped off by her son in Atherton on December 29, telling him she was going to the local hotel to play pool and visit a friend.
A police investigation revealed she attended the Atherton Hotel bottle shop and left in the company of two men.
A 2014 coronial inquest found Ms O'Shea likely died soon after December 29 in the Atherton Tablelands area.
"Katie was known as a happy, fun-loving and devoted mother," Det Devine said.
"Her children haven't had a mother for the last 18 years.
"On top of that they don't know how their mother disappeared...so that's an added burden for them."
He said the reward marked a "significant day" for Ms Parmenter and her family.
"It (reward) shows that this investigation is not closed and it will remain open," he said.
"We believe a person or persons are responsible for her death.
"Half a million dollars is a lot of money. It may prove an incentive for someone to just make that phone call."
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