Kirsty and Aaron McConnell lost their 18-month-old daughter, Lily, to a form of motor neurone disease called spinal muscular atrophy in March.
"To watch your baby struggle to breathe and struggle to do normal baby things, that was very difficult," Ms McConnell told SBS News.
Both parents said they had healthy children from previous relationships and no family history of the disorder.
"We had no clue at all of our genetic makeup that we could potentially be carrying a mutated gene," Ms McConnell said.
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Researchers at the Murdoch Children's Research Institute have screened about 12,000 people for cystic fibrosis, fragile X syndrome and spinal muscular atrophy.
Investigator Dr Alison Archibald said the researchers found it was common for anybody to be a carrier of one of three conditions - spinal muscular atrophy, cystic fibrosis and fragile X syndrome.
"You really don't need a family history to be a carrier and the affected pregnancy rate is very similar to that of Down syndrome," said Dr Archibald, who is a genetic counsellor at the Victorian Clinical Genetics Services - a subsidiary of the institute.
The screening showed 88 per cent of the study's participants had no family history of any of the three conditions.
Murdoch Children's Research Institute clinical geneticist Professor David Amor said one in 240 couples had an increased risk of having a child with one of these disorders, and about one in 1,000 pregnant women screened had a child born with one of these conditions.
A saliva or blood test can reveal whether a parent is a carrier for these disorders - pre-pregnancy or in the early stages - giving parents time to consider their options.
Dr Archibald said these tests should be offered.
"This is the ideal test for GPs to offer to couples to come to them and say, 'We're thinking about having a family, what do we need to do to prepare?'" she said.
But the Australian Medical Association cautioned parents should be properly supported.
"The most important thing to understand about any genetic testing is that it should be done in a setting with people who can counsel the person receiving the result of the test appropriately," AMA Victoria's Dr Lorraine Baker said.
