I would have to say that I disagree that Eliza, from Shaw's Pygmalion represents the new woman.
Eliza does not wish to change herself until it is brought to her attention that she needs to be changed. Therefore, she does not represent the new woman because the new woman makes this decision on her own.
The new woman is a strong woman who does not need the guidance or help of another in order to better herself. She possesses the inner strength and determination to decide what her own weaknesses are and the need to change them. She does not need to be told to do so.
Also, Eliza was shocked to find that Higgin's loses interest in her after the bet has been won. The new woman does not depend, or rely upon, another to need her. She is strong enough to stand on her own two feet and support herself.