Why has the author chosen this title?
This title is both ironic and appropriate. Nora's husband often treats her as if she is a child rather than a grown woman. Her home and her ability to function within it as an adult are limited to this idea of her as a childlike woman, who can't make her own mature decisions. Torvald, her husband, chides her for spending money or being frivolous, and controls most aspects of her life. He also criticizes her attempts to help her friends, acting as if she lacks good judgment. The idea of a husband as a protector creates the illusion that a woman needs protecting, and cannot be strong on her own. She is indeed like a toy or plaything within her own home. Nora finally realizes she lacks autonomy and courage, confronts Torvald, and finds a way to go forward with her life on her own.
The above answer is excellent. It might be added that a doll's house is delicate and fragile, subject to being damaged or destroyed. I am reminded of Tennesse Williams' play The Glass Menagerie, which has a similar symbolism.