In The Princess and the Goblin, Princess Irene's character changes over the course of the narrative, and she becomes more daring, resilient, and resourceful in response to the difficult and frightening situations she faces.

One reason you might give in support of this thesis statement is that MacDonald tells the reader at the beginning of the story that the "sweet" young princess was compelled to grow up very fast. In the second paragraph, he writes:

The princess was a sweet little creature, and at the time my story begins was about eight years old, I think, but she got older very fast.

At the end of chapter 2, the reader can see this development happening, as Irene masters her fears, which are only natural in the circumstances:

At last her hope failed her. Nothing but passages and doors everywhere! She threw herself on the floor, and burst into a wailing cry broken by sobs.

She did not cry long, however, for she was as brave as could be expected of a princess of her age.

Irene quickly becomes considerably braver than could be expected of any eight-year-old girl. By the beginning of chapter 20, she responds to frightening events with a quick wit and resourcefulness well beyond her years.

That same morning early, the princess woke in a terrible fright. There was a hideous noise in her room—creatures snarling and hissing and rocketing about as if they were fighting. The moment she came to herself, she remembered something she had never thought of again—what her grandmother told her to do when she was frightened. She immediately took off her ring and put it under her pillow.

It is partly the influence of Curdie, who is several years older, which causes Irene to grow up so rapidly. However, even when she does not have Curdie's help, she keeps her nerve to a remarkable degree. By the end of the novel, she is bypassing Lootie to talk to her father, the king, as an equal.