In Act 1 of A Doll's House Mrs. Linde describes Nora as a 'child.' Is this assessment of Nora's state of development valid?

The first impulse is to agree with Linde and say that Nora is, indeed, a "child." However, upon a deeper reading into Nora's character,  it would be unfair to think that. 
Linde, as well as everyone else mentioned in the play, is only aware of who Nora is through the image that Nora chooses to give of herself; that of a carefree, immature, playful and ornamental part of the household. It is no surprise that Linde would think of Nora exactly as the type of character that Nora so eagerly portrays.
Still, after having been friends with Nora for years, one must wonder why Linde continues to assess Nora's character based on these external traits. The answer to this is that Linde had not learn about the sacrifice that Nora had to make years earlier in order to save the life of her husband. Entering in a business loan deal with Krogstad,a man who is beneath her husband's own status, and to do this behind her husband's back, was beginning to get back at Nora in a very bad way. 
Therefore, Nora was, indeed, going through a very difficult situation that would have required a huge amount of "adulting" to do, that is, she would have had to make choices and decisions that a mere "child" or immature person could have never been able to do. Hence, Linde was not being 100% fair when she called Nora a "child." 
Remember also that Mrs. Linde and Nora had not seen one another in years by the time that Linde visits Nora, hoping to get a job at the bank where Torvald works. Linde has fallen in hard times, is much older than Nora, and has gone through terrible vicissitudes in life that have rendered her a very objective, no-nonsense type of person. 
Linde had always known Nora for being sort of an opposite of Linde: Nora had not suffered, in Linde's opinion, any of the life tragedies that make people grow up and mature. To Linde, Nora had always been given everything that she wanted, and her problems are minor, at least compared to those that Linde has gone through.

How kind you are, Nora, to be so anxious to help me! It is doubly kind in you, for you know so little of the burdens and troubles of life.

To this, Nora seems to disagree, and then Linde explains

Linde [smiling] My dear! Small household cares and that sort of thing!--You are a child, Nora.

Nora disagrees, and resents that Linde, of all people, would think such an opinion of her. In fact, we see Nora resenting more and more that image that people have made of her, even though she has worked more than hard to build that image all by herself.