Coroner Christopher Devonport last week said the death was a tragedy and a timely warning to parents to secure heavy objects.
Ms Malcolm-Black said there were three key things parents could do to help prevent youngsters' falls.
"Changing children on the ground, or making sure one hand is always on their child when they're on a high surface, having barriers at both the top and bottom of stairs, and not using baby walkers.
"They're dangerous because they can tip over, fall down stairs or move quickly into danger such as towards a heater or stove," she said.
Plunket national child safety adviser Sue Campbell said that, unfortunately, it wasn't possible for parents to keep an eye on their children 24/7.
"When things go wrong, it's a reminder for anybody, 'Gosh, I need to do something about that'. You can't childproof a home ... you can do the best you possibly can, but kids are kids and you can't make a home totally safe."
Dangers faced by children in and around the home varied depending on their age, Ms Campbell said.
"What we talk about a lot with preventing accidents is thinking to what stage of development that baby or child is going to get to next."
Plunket encouraged parents to prepare for potential risks in the home, such as ensuring a fire guard was in place before a child started crawling, or putting a barrier at the top of stairs before little ones became more mobile.
Bracketing existing appliances and furniture and favouring wall-mounted options when buying new devices all helped, Ms Campbell said.
"You can't - in spite of the fact you'd probably like to - watch them every second that they are around. It's about doing the best that you can."
Plunket's Thriving under 5 book is given to new parents at their first Plunket visit. It tells how to make a home safer for a child. APNZ
