Aristea loves her grandmother dearly. Much of her childhood has been spent at her the Northcote home of her 'yiayia', eating stuffed tomatoes and cheese cake, doing homework and trading secrets in Greek.

So it took enormous strength for the 12-year-old to fight for her yiayia's right to die.

"If she wants to end her pain, I think that's her choice."

Aristea's grandmother has told her family she no longer wants to endure the severe, relentless pain of untreatable osteoarthritis. She feels anxious about the next time her pain will become unbearable, and says wants the option to put a stop to it.

"At first, I felt a bit sad. I thought, she wants to kill herself," Aristea tells Fairfax Media.

But the grade six student has grown increasingly distressed by her grandmother's deteriorating condition. She decided she had to act.

So she wrote to Prime Minister Malcolm Turnbull, demanding he change the law.

In a strongly worded three-page letter, she argues that terminally ill Australians were resorting to "repulsive", inhumane methods to kill themselves.

She compared the situation of a terminally ill Australian patient, forced to consider starving themself to death, with that of a "cancer victim in Luxembourg [who] rests peacefully in his hospital bed, holding his family's hands and ending his life harmoniously," she said.

"It is utterly appalling how extremely ill patients are required to put themselves through more unnecessary pain. How can people allow this?"

"Like the yin and yang or two sides of a coin, human life cannot occur without death.

"Consequently, those who argue that every human has the fundamental right to live, unknowingly also consent to the fact that every human has the rudimentary right to die."

Aristea also argued that people should have the right to a life of quality, rather than quantity "by allowing people to determine the how and when of their death, we are guaranteeing they will live what remaining life they have to the fullest; free from the pain of anxiety."

12-year-old Aristea with her grandmother Voula. Photo: Pat Scala

Her grandmother, Voula, showers her with life lessons: study hard, enjoy life while you're young, and fight for what you believe.

The 79-year-old grandmother is growing weak, becoming bedridden for weeks at a time. She is responding poorly to medication and unfit to have surgery.

The grade six student wrote to the PM about the issue as part of a project at Clifton Hill Primary School.

"Euthanasia is currently in favour of the country, and has been since 1964. Not respecting these wishes that your citizens hold will no doubt, in their eyes, demote you," she wrote.

Aristea points out that euthanasia is legal in the Netherlands, Switzerland, Belgium, Luxembourg and some US states.

A recent Victorian parliamentary report recommended the state government legalise assisted dying for people suffering from serious terminal conditions.

But Mr Turnbull has indicated he does not support euthanasia, while Labor and the Greens have said they would allow their members a free vote.

Aristea, who also sent her letter to Premier Daniel Andrews, said the Prime Minister still owes her a response to another letter she sent him, in which she suggested changes to the design of wind turbines.

(She has also interviewed Alex Bhathal about "active citizenship" earlier this year, in between playing piano, the cello, and writing a crime story.)

"If he [Mr Turnbull] doesn't respond it's like he is avoiding it. And, I took a lot of time on it, so I think that he should be able to notice that and take some time to reply … I hope he will."

Read the full letter here:

timna.jacks@fairfaxmedia.com.au