How can I support her head when my child has fallen asleep?

There are different options: for small children, the edge of the wrap can be folded over a small piece of fabric, e.g. a muslin cloth, to make a head support. If the child falls asleep on your back, a doll sling can be used to stabilise the head. Here, too, it is a matter of trying things out and, if necessary, having the various options shown to you in a babywearing consultation.