The World Health Organization's has released guidelines for vaccination - including who should and should be vaccinated right now. Click the link below to see what they say about vaccinating children:
COVID-19 advice for the public: Getting vaccinated
UPDATE: Since this post was published, the WHO has altered their recommendation to: "More evidence is needed on the use of the different COVID-19 vaccines in children to be able to make general recommendations on vaccinating children against COVID-19," rather than recommending children should not be vaccinated.