Yes, children can travel on Airbnb, but some hosts have specified that their space may not be safe or suitable for children or infants.
Infants (children under 2 years old) are not counted as guests when you're booking a reservation and wouldn't incur any extra costs.
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Now I have changed my rules not to offer accommodation for children under 2 years of age, even though my house is a favourite with families with children of all ages. I am hoping to get these families to find me on other platforms. Once you check off that you do not accept children under 2 years of age the searches are filtered and families looking for accommodation will not find your listing if they enter that they have children under 2 years of age.