Well, I think there were several things involved that helped her overcome her fear. In the first place, she felt safe at home, so putting the subject of fear (puppy) in the safe environment where nobody else had a problem with it what she could clearly see, if nothing else, probably confused her first fear impulse and caused its absence.
Secondly, nobody was asking her to interact with the puppy. It was just there and she could approach or not, or even walk away.
Despite all of that, I believe the crucial role played her brothers. The older one as always protectively oriented when his younger siblings were in question that probably gave her some additional feeling of safeness. While the younger one encouraged her from the opposite side. As the two years older sister, she was already used to teach him many things. So, I think she must have been confused but as well curious and provoked how her younger brother who was supposed to learn from her was getting along with that puppy so well and much better than she does.
I believe that must be the main triggers that lead to the positive outcome, of course, not to neglect as well the good Christmas energy when all started.