A GoFundMe, launched by Perth's Rwandan Community Abroad (RCA) group to help cover funeral costs, has already raised close to $8000.
"The African community is saddened with the news of the loss of a young child in our community," RCA said in a statement.
"We would like to take this time to send our heartfelt condolences to the family who's going through a tragic period of grief and loss.
"We encourage our community members to be there for one another and provide as much support to the affected family.
"This GoFundMe page has been created to support the affected family in raising funeral funds for our beautiful baby Tayla. Any support you can give is greatly appreciated. We also urge our community and extended communities to please respect the families (sic) privacy during this difficult time."
Roughly one child will die and 30 children are rushed to hospital each year in Australia after being injured by furniture.
Kidsafe WA advises parents with young children should buy low furniture, and use straps or affix their items to the wall where possible to prevent furniture from falling.
It is not yet known whether the chest of drawers had been secured to the wall.