"What happened down in the dungeons between you and Professor Quirrell is a complete secret, so, naturally, the whole school knows."
Albus Dumbledore to Harry Potter, PS17
Harry finally wakes up in the Hospital Wing days after his faceoff with Quirrell. Dumbledore fills in some of the ambiguities that still remained for Harry and his friends after all they discovered. Following his talk with Professor Dumbledore, Harry is released from the Hospital Wing and allowed to attend the end-of-term feast. (PS17)
Among the things Dumbledore tells Harry are: he was protected by his mother’s love and sacrifice; he should say Voldemort’s name, rather than give in to fear; Nicolas Flamel and his wife, Pernelle, have enough Elixir of Life set aside to put their affairs in order but will die now that the Philosopher’s Stone has been destroyed.
Dumbledore has the perfect moment to tell Harry all about Trelawney's first prediction - when Harry actually asked the key question - but let the moment pass because he cared more about allowing Harry to have a childhood than about the fight against Voldemort, at that moment.