Babies can safely sleep with a blanket after their 1st birthday but I would wait until the baby was at least 13 to 14 months before giving them a blanket to prevent the risk of suffocation.
After a year old most babies are okay with sleeping with a blanket and a plushy toy but not before then.
If you want to keep your baby under 1 year old warm you can have them sleep in blanket sleepers or other warm pajamas.
Also a baby should sleep in a crib or baby bed until they reach 2 years old to keep them safe and then after 2 years old the toddler can then move to a toddler bed or regular bed.
A baby needs to be able to roll themselves over and back again to prevent suffocation before they sleep with a blanket.