Can a 12-month-old child recently vaccinated against chickenpox transmit chickenpox to another child in the same daycare?

No, a child who has recently been vaccinated against chickenpox cannot transmit the virus to another child in the same daycare. When a child receives the vaccine, they do not actually get the illness but rather develop immunity to prevent getting infected later on. It is just a coincidence that the two events happened around the same time.