Maddie is, of course, flying to Scotland on military business—so mentioning
Peter Pan like this seems to be a way to make the war seem less serious (and, in turn, easier to handle). Jamie bringing up “The Pobble Who Has No Toes” suggests that Maddie isn’t the only person engaging in thought exercises like this—referring to Jamie in this way helps soften the fact that he lost his toes to frostbite. Especially when considered alongside Jamie’s mother leaving the windows open like Mrs. Darling, it suggests that this practice of reverting to an innocent or childlike worldview is somewhat widespread.