Ms Dixon, 22, spent Tuesday night making people laugh at the CBD's Highlander Bar but less than a kilometre from home she was raped and killed in North Carlton's Princes Park.

Broadmeadows 19-year-old Jaymes Todd has been charged with her murder.

It's been reported as she approached her home she had messaged her boyfriend "I'm almost home safe HBU (How about you)".

Premier Daniel Andrews took to social media on Friday to remind people Ms Dixon died because of her attacker, not her own actions.

"Go about your day exactly as you intend, on your terms, because women don't need to change their behaviour. Men do," he wrote in a Facebook post.

But Police Minister Lisa Neville and Melbourne Lord Mayor Sally Capp admit they do not always feel safe themselves.

"I want women, and as a woman, I want to be able to be safe in my community, I want to be able to walk through the streets, I want to be safe at home and unfortunately that's not the case," Ms Neville told reporters.

Ms Capp told 3AW radio she would not feel safe walking around at night.

"But at the end of the day, we should all be able to move around our city safely, and so focusing on the actions of those committing these crimes is very important," she said.

Victoria Police will be at Princes Park from 10am to 2pm on Saturday to discuss safety concerns with the public, along with the Red Cross and Victorian Council of Churches counsellors and support people.

A vigil will be held on Monday evening at Princes Park, aimed at reclaiming the public space where Ms Dixon was found.

Organiser Pia Cerveri, who works at Trades Hall women's team, told AAP it's about paying tribute to Ms Dixon while emphasising the right of all women to use public spaces without fear.

Chief Commissioner Graham Ashton said people should have the right to walk alone late at night, but it was more a question of assessing risks.

"If you're driving a car, you don't speed, you drive that car safely and we always have attention to our safety," he told 3AW.

"This is really a similar thing where we always need to make those assessments of our safety when we're going about the community because events like this, whilst rare, can occur."

Mr Ashton said it is natural such a crime increases community fear, just as it did with the murders of Jill Meagher in 2012 and schoolgirl Masa Vukotic in 2015.

Meanwhile, Melbourne's comic community has rallied in tribute to Ms Dixon, with comedian Chris Franklin posting on social media that she will be remembered at the Highlander Bar, where she performed the night she was killed.

Todd will reappear in Melbourne Magistrates' Court in October.

His father Jason Todd told Fairfax his family were in shock and offered Ms Dixon's family "our deepest condolences".

Australian Associated Press