This is how I fancy the scene:

1) during the time between Hertfordshire and Rosings (ie winter), Darcy, so far not realizing he is falling in love with Elizabeth asks his sister whether she knows a certain piece of music... and then explains that he heard it played by a young lady in Herts'... and then he can't avoid mentioning her very often (thus paving the way for his falling in love at Rosings when he notices that she is aven wittier, prettier than in his memory... above all when far from her wearisome family), and Georgiana keeps asking about her who, she believes, must be some sort of a model in a woman, since her brother admires her.
2) In a letter written from Rosings, he has to tell her that to his surprise that young lady he heas spoken of is here and makes their stay less boresome.
3) Back from Rosings, he is dejected. Georgiana dares not ask Darcy any questions, but she pesters her cousin with queries as to what has happened, and she finally guesses what happened (though she cannot understand how anyone could reject her ideal brother). Maybe at a time she dislikes Elizabeth for making him unhappy, but when she voices her feelings, he tells her that indeed Elizabeth is the paragon of pêrfection.