"Dolly's passing highlights the devastating impact that bullying can have on its victims", Turnbull said.
The great-grandmother of Amy "Dolly" Everett has moved family and well-wishers to tears with her emotional reading of an original poem at the teen's memorial service.
"She was loved by so many and made friends with everyone she came across".
The family nicknamed her Dolly because mother Kate thought she looked like "a flawless little china doll, Dolly just stuck", Mr Everett said.
Given that it was also on social media that Dolly received abusive messages, her father's wish is that those who tormented his daughter from behind screens could see, in real life, the painful consequences of their actions.
He said she "loved anything that had four legs and a heartbeat... if she could raise it she'd do it". "Let's stop the bullies, no matter where, but especially in our kids", he wrote.
Dolly's family, meanwhile, has set up a trust called Dolly's Dream to raise awareness of bullying, depression and youth suicide.
"We don't want another family to go through what we are going through and our vision is to establish a trust called Dolly's Dream", the family said.
"It won't bring our Dolly back, but it may just prevent the loss of another young life."
Before her tragic death, Dolly wrote "Speak even if our voice shakes" which has become rallying cry against bullying.
Dolly, from a well-known NT grazier family, died on January 3. He asked for them to attend her funeral.
After the service, mourners released balloons and butterflies.
Australian Prime Minister Malcolm Turnbull on Thursday night issued a statement on social media, saying his heart was breaking for the Everett family.
The Queensland boarding school that Dolly attended, Scots PGC College, has said the welfare and privacy of the entire school community remained its priority during this hard time.
Earlier on Friday, Northern Territory police confirmed they were investigating the circumstances surrounding Dolly's death.