Infants are generally not vaccinated in the first few month but would have most common shots by the age of 1, with refreshers up to the age of 2. However they

Infants are generally not vaccinated in the first few month but would have most common shots by the age of 1, with refreshers up to the age of 2. However they do get protected by what’s called “herd immunity” If a sufficient fraction of all other people are vaccinated, diseases cannot spread. So basically the toddler in the family gets protected because the older kids/parents cannot be disease carrying. So yes, anti-vaxxers are a problem for toddlers (and other people that cannot be vaccinated due to other reasons)