"Brienne accepted her knighthood from Jaime with perhaps her first moment of unbridled joy."
I wonder if her joy had more to do with being knighted, or the person knighting her. At Joffrey's wedding, Cersei says she can tell Brienne is in love with Jaime. Brienne seemed shocked but did not disagree. I think she struggles with that still because she never thought romance would be an option for her. And now the man she loves is not only asking to serve her, but made her a knight.