The trio were walking on a footpath when a 91-year-old driver lost control of her car in Wantirna South, in Melbourne's east, on Thursday.
A 59-year-old woman died at the scene while a 60-year-old man suffered life-threatening injuries. A two-year-old boy was seriously injured and is in a stable condition in hospital.
Detectives are yet to interview the elderly driver, who they say was shaken by what happened and suffered only minor scratches.
Her Toyota Yaris mounted a footpath and hit the trio before travelling down a hill and smashing through a fence, finally coming to rest after hitting a bench.
Superintendent Justin Goldsmith said the adults and child, who are believed to be related, were walking in the same direction as the car was travelling when it struck them.
The out-of-control car continued down the road for another 200m, hitting a street sign and running through the fence near a playground.
Victorian acting Premier Ben Carroll said the tragedy brought into focus previous calls for older people to prove they're fit to drive, in line with rules in place in other states.
"It is a valid question that you raise around testing," he told reporters on Friday.
"I will work with the road safety minister on this."Â
Victoria does not have age-based driving safety requirements, although drivers aged 75 and older must renew their licence every three years, which can involve various tests.
NSW, Queensland, the ACT, Tasmania and the Northern Territory require drivers older than 75 to have a health check, while older drivers in South Australia must complete self-assessments.
In Western Australia, an annual medical assessment is required to renew a driver's licence after turning 80.
But the peak body for GPs said mandating annual medical checks for drivers was not the solution.
"A person may pass a test on a day with their GP, but that doesn't mean that every single time they drive they don't need to ask themselves, 'is it safe for me to drive today and in these conditions?'" Royal Australian College of General Practitioners Victoria chair Anita Munoz said.
Australian Road Safety Foundation chair Russell White has called for a nationally consistent approach to age-based driving requirements, but said there needed to be a staged approach across age groups.
"The hard thing dealing with human beings is that everybody's going to have a different level of ability as they age," he told AAP.
Australasian College of Road Safety chief executive Ingrid Johnston said authorities needed to support older drivers with opportunities to maintain safe driving and alternatives when that may no longer be possible.
This could include medical and cognitive testing or skills testing with training programs specifically designed to help them maintain safe driving.
The crash happened during the first week of Victorian school holidays, bringing deaths on the state's roads to 14 in the past seven days.
In November, a kindergarten worker was killed and a three-year-old boy injured when a runaway truck smashed through the gate of Macedon Ranges preschool's playground.
Two weeks earlier, an 11-year-old boy was killed and four other students injured when an SUV crashed through a fence at Auburn South Primary School in Melbourne's east.
