Yes, you can give melatonin to a 1-year-old child who is having trouble sleeping. It is often suggested for children aged 6 months and older in the short term. You can try a dose of up to 3mg once a day at bedtime and increase if necessary. Melatonin is a hormone that the body naturally produces to regulate the sleep-wake cycle. It may have an immediate effect, but it could take several weeks to reach maximum effectiveness. However, we may not know the long-term effects, as data for adults only go up to 6 months. Good luck and hope your child sleeps better soon.