Yes, they’re safe. The vaccines have been studied and tested extensively for all age groups. The dosage for the 6 months to 11-year-old age group has been adjusted to ensure that children are receiving the correct amount of vaccine for their age, size, and immune system. Children in all age groups were monitored for weeks and months following their vaccinations, and during the preauthorization trials no serious vaccine-related health problems were reported.
COVID-19 vaccination efforts are being monitored more closely than any public health initiative in US history. Safety studies have included children and adolescents, and show the vaccines are safe for this age group.
https://www.muhealth.org/our-stories/how-do-we-know-covid-19-vaccine-safe-kids (Michigan University)