Yes, Australian children, including newborns and minors, require a visa to enter Laos. Children's visa requirements are essentially the same as those for adult Australian nationals.
Citizens of Australia can apply for a Laos e-Visa online. The e-Visa permits you to stay in Laos for up to 30 days and is valid for a single entrance.
Here are the requirements for a Laos eVisa for Australian citizens: