How does Gretel's loss of innocence help her survive?

In the story, Gretel is actually as naive as Bruno is in regards to Out-With and the circumstances surrounding Jewish incarceration. However, because of her tendency to exude what she considers an air of nonchalant sophistication, Gretel's innocence is not as apparent. Gretel hides her naivety behind a facade of sarcasm, irritation, and denial.
By Chapter 16, it is obvious that Gretel has lost her innocence. She no longer plays with her dolls. In their place are maps of Europe. Gretel now spends so much time poring over them that Bruno fears for her sanity. The text tells us that "every day she put little pins into them and moved the pins around constantly after consulting the daily newspaper." It appears from Gretel's actions that she is tracking the course of the war on the maps.
Gretel's loss of innocence helps her survive but in a negative way. She survives by adopting and cherishing the same bigoted views that have resulted in the mass slaughter of innocents. Because of her youth, Gretel is unable to process her loss of innocence in a constructive way. So, she resorts to the same illogical prejudice that is championed by German leaders. When questioned by Bruno, Gretel cannot explain why Germans must hate Jews. 
In fact, she cannot even explain what being a German means. All Gretel knows is that Germans are the "opposite" of Jews. She understands that Germans are to hate Jews but not the reasons for doing so. So, Gretel's loss of innocence helps her survive by reinforcing what she has been programmed to believe.