The answer to this question poses a very subjective answer. While some may agree that Eliza does represent the "new woman," others may disagree.
On one side, Eliza has become a woman of the times--educated, well-spoken, and dignified. On the other hand, others may believe that Eliza was much better off as she was--a street-smart woman with quick wit and natural intelligence. Therefore, the answer would depend upon how one sees Eliza at the end of the play.
While she becomes more dignified and a well-spoken woman, does her "education" allow her to represent the "new woman?" In essence, Eliza does come to understand that how one is measured by society relies upon how society treats the person. Eliza realizes, after the bet has been won, that Higgins begins to lose interest in her. It is not Eliza which ignites interest in Higgins; instead, it is the challenge alone.
That being said, I do believe that Eliza does represent the "new woman." Her thoughts on society have changed because of her "education" and she has come to realize that some things are simply left better as they were. Therefore, Eliza's new knowledge about the world around her has transformed her into a more enlightened person. By being enlightened, Eliza has become a new woman.