ben in slingThis is one of those areas where authenticity gives way to safety; this is because medieval babies up to 6 months and occasionally a year old were swaddled. Swaddling is the practice of wrapping the baby tightly in strips of cloth so that it can't move; as it got older sometimes its arms were freed. However, I would never recommend ever swaddling a baby, because most of their bones are still soft and the practice can cause permanent damage to the child's limbs. Also, can you imagine the reaction most babies would have to being tightly wrapped in such a way!
Instead, I suggest a full length shift and possibly a tabard style tunic and blankets if it's cold. To keep nappies covered up, I would recommend a piece of linen or muslin wrapped around. You could also use a spare scrap of material for a sling. A coif is also useful if it's cold, if the child will keep it on. If it is hot, loosely cover the baby in about a square meter of linen. Basically just try your best to keep your baby happy!