In The Great Gatsby, when Daisy pretends that she is happy her baby is a girl and that she hopes she is a "beautiful little fool," she is stating that she is aware that virtually the only opportunity for advancement a woman has in patriarchal America in her day is to act stupid and be pretty. Daisy is stating the reality of her situation, and of the situation her daughter will face.
Daisy is intelligent and witty, and she's smart enough to know how to survive as a woman in a male-dominated world. The American Dream is, for the most part, inaccessible to a woman. The only chance a woman has is to be a beautiful little fool.
Daisy is really disappointed that her baby is a daughter:
She [the nurse] told me it was a girl, and so I turned my head away and wept.
In a display of despair, she then says:
'All right,' I said, 'I'm glad it's a girl. And I hope she'll be a fool--that's the best thing a girl can be in this world, a beautiful little fool.'
Daisy's daughter's only shot at the American Dream is to act stupid and look pretty and marry a wealthy man. Men have other choices in the world of America in the 1920's, but the women do not seem to.
Daisy says this in Chapter 1. She says that she wants this because it is the best thing that a girl can be given the way the world is.
To me, this shows that Daisy is a very passive person. She does not want to get out and be her own person. Instead, she would prefer to just sit around and have men control her life. This makes her seem very shallow and weak to me from my modern point of view. I think it is likely that she would have looked different to a reader at the time when this book was written and many more people probably expected women to act this way.