Is Daisy, within The Great Gatsby, designed to be a "silly" or "ditsy" character? If not, why does she do "silly" or "ditsy" things?
Your question concerning The Great Gatsby is a little difficult to interpret. How is she so silly? Do you mean why? I'll assume you do and answer accordingly.
There are numerous answers to your question, depending on one's interpretation of Daisy. I believe Daisy has learned to appear silly and ditzy in order to get along. How else could she get along with Tom? He would not tolerate a woman thinking for herself.
The most important piece of evidence that Daisy just acts silly and ditzy is what she tells Nick in chapter one about her daughter. She was hoping for a boy but had a girl instead. She sarcastically tells Nick that she was glad it was a girl, and that she hoped she was a beautiful little fool, because that's what it takes for a woman to succeed.
The idea is that a woman's best hope for social and economic advancement in a society dominated by men is to marry a wealthy man, and the odds of doing that go up if one is a beautiful little fool.
Of course, that's what Daisy has done--pretended to be a beautiful little fool and "caught" a wealthy husband.
And that's why Daisy acts like a silly little fool.
In many ways Fitzgerald leaves a great deal out of the story and it is difficult to find a whole lot of substance in Daisy's character, thus the sense that she is ditzy or empty. She also clearly represents the idea that money is the key to happiness and can make everything work out the way you want it to. As such, she is in many ways supposed to present the picture of silliness given that the novel in many ways seeks to point out the emptiness of money and the destruction wrought upon Gatsby because of his headlong quest for it and its society.
The short answer is that she was in many ways designed as a character to be ditzy and silly.
Daisy is a foolish woman, a spoiled woman, and a lonely woman. When you add these elements together, she may seem silly but she is actually confused and - in many ways - apathetic to the world. I see her depressed and vunerable, unable to handle her wealthy but boring life. She masks that vunerability by acting silly.
Yes, she is outwardly ditsy, but answering this question in an assignment would require deeper analysis and soul-searching on your part. I don't know that there is a direct answer, as Daisy is a fascinating character, and fascinating characters generally have many layers to unpeel. In the end, your own opinion would matter the most.
Reading the book, along with watching film adaptations, can help you understand Daisy more deeply. The links below will direct you to information about the 1970s film adaptation and an online copy of the novel.