I have to agree in that Nora would be "the doll" because, as a doll, she is expected to be sweet, cute, girly, and perfect. Unlike Helmer, she was actually given every element possible to allow this to happen: The house, the pet kids, the treatment (most of all), and the illusion of it all being "alright."
Helmer was decidedly less fortunate than Nora, and if she were to play the role of a doll it would not be as credible nor effective as a stylistic choice given that none of the expectations placed on Nora were placed on Helmer.
Either Noraor Helmer could be considered the "doll" in Ibsen's A Doll's House. They both, at one time or another, play the part of the stereotypical gender role which Ibsen rallies against. Nora plays such a role prior to the play itself and presents herself as an act of rebellion against her former behavior throughout the play. Helmer, however, maintains his stereotypical role throughout the play. The central purpose of the play is to explore these stereotypes and the natural bias and hypocrisy involved in such thinking.
When I was introduced to the literary concepts in the play "A Doll's House" I was originally taught that Nora was the doll. She had grown up in a world controlled by men. Men had moved her from situation to situation. She was her father's daughter and his expectations, means of supporting the family, and dominance over the family shaped her into the wife who moved room to room in the doll house.
After she marries she is just the same woman moved into another doll house where she is moved around to look pretty, be pleasant, and be what her husband expected her to be. She is not really meant to be her own person. She is merely a figure again, a doll controlled by men.