Xavier wants to see if his daughter knows that she exists. while he is wiping her face, he puts a red dot on her nose and then shows her own reflection in a mirror. at what age would we expect her to reach up and touch her own nose instead of reaching for the nose in the reflection?

According to researcher Daniel Stern, at about 18 months children begin to develop a sense of self-awareness, including recognizing themselves in front of a mirror, their use of labels for "self" and empathic acts. He says that:

"Prior to the age of eighteen months, infants do not seem to know that what they are seeing in a mirror is their own reflection. After eighteen months, they do. This can be shown by surreptitiously marking infants’ faces with rouge, so that they are unaware that the mark has been placed.  When younger infants see their reflections, they point to the mirror and not to themselves. After the age of eighteen months or so, they touch the rouge on their own faces instead of just pointing to the mirror" (The Interpersonal World of the Infant, 1985, p. 165).