Ms Nelson, 37, died alone in her cell at the Dame Phyllis Frost Centre in January 2020, with a coroner later finding her death was preventable and the state's bail act needed reform.
Ms Nelson's family on Wednesday called on the Andrews Labor government to legislate changes, including removing the presumption against bail and scrapping of all bail offences.
The reforms should be called Poccum's Law, in reference to Ms Nelson's nickname and won't receive the family's blessing if they fall short of their demands, her mother Aunty Donna Nelson said.
"I want these reforms to be made in honour of my daughter Veronica so lawmakers can always be reminded of how cruel and inhumane prison can be to our mob," Aunty Donna said in a statement.
"The Victorian government has an opportunity to get this right once and for all."
The Gunditjmara, Dja Dja Wurrung, Wiradjuri and Yorta Yorta woman was wanted over the theft of perfume from a chemist when she was picked up by police in Melbourne's busy Spencer Street.
Ms Nelson, who was suffering from severe opioid withdrawal, begged for help over the intercom 49 times in the 36 hours before her death.
While passing on her condolences to Ms Nelson's family, Attorney-General Jaclyn Symes said the government wasn't considering their demand to completely remove the presumption against bail.
"We know there has been a disproportionate impact on some vulnerable groups and we're seeking to address that," she told reporters on Wednesday.
The government was consulting on the proposed laws and nothing was necessarily ruled in or out, Ms Symes added.
The push comes as a new report from the Justice Reform Initiative shows the number of Indigenous people in Victorian prisons rose in the past decade from 6.2 per cent to 12 per cent of total inmates.
Indigenous adults were imprisoned at 15.6 times the rate of non-Indigenous people, despite making up one per cent of Victoria's population.
Overall inmate numbers also rose 32 per cent in the past 10 years, while corrections spending increased 96 per cent.
More than half of those locked up had been there before and people on remand made up 42 per cent of the prisoner population.
The Justice Reform Initiative, which includes former MPs, Indigenous leaders, judicial figures and other experts, is calling for evidence-based policies to reduce numbers and save taxpayer money.
Victoria's "revolving door" system costs $1 billion a year to operate and that money could be better spent on post-release programs to reduce reoffending, executive director Mindy Sotiri said.
"There's not a single magic reform fix," she said.
Legislation to reform Victoria's bail laws, child protection and youth justice system will be brought before parliament in the first half of this year.
Former Victorian attorney-general Rob Hulls said the coroner's report into Ms Nelson's death provided a "roadmap" for the government and opposition to change their tune.
"Often what happens at election time is politicians will stand on the front steps of parliament house with their law and order baseball bat and say 'vote for me, my baseball bat's bigger than his or hers' and 'my bat is going to make you safer as a community'," he said.
"But all the evidence shows that's not the case."
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