In Act I, Eliza is a young hustler, trying to sell flowers on the street. She is pretty pushy about selling her flowers and takes advantage of Freddie's obvious guilt in having knocked her over and spilled her bouquets. She presses Freddie's mother into eventually buying her flowers, despite the protests of Freddie's sister. She is not deterred by the fact that it is raining but continues to hustle her flowers when she is startled to discover Higgins behind her taking notes. At first, she believes he is a policeman because he is writing down her words. She reacts literally to everything he says. When he recognizes her dialect and identifies that it is from Lisson Grove, for example, she reacts by defending herself for having a right to leave Lisson Grove because it was not a nice place to live. She is totally naive to what is really going on in this Act and her character here is very stereotyped. She falsely believes that Higgins has insulted her in the beginning, but then when he really insults her by mimicking her way of speaking and the sounds she makes, she is amused. Higgins winds up throwing money at her for her flowers and instead of saving it and bringing it home for food or something practical, she hails a cab and majestically announces to Freddie, who has reappeared, that she is going home in a cab, like a lady.
You can read the play here on eNotes and see if you agree. We do not see any depth in her character in this Act.