My child is 11 now but will be 12 when we go to Japan. Is he/she eligible for the JR children pass?

Yes, children who are 11 years of age at the time the Exchange Order is issued are eligible for the discounted child Japan Rail Pass.

The general rules of JR Group state that children from the ages of 6 through 11 are eligible for the discounted Japan Rail Pass. Those who are under 6 years old don't require a Japan Rail Pass as they can travel for free. However, seat reservations are not available for children under the age of 6.