She is that sort of a person who prefers to have more time on her hands so as to avoid the last-minute rush.

rush 在这里是名词，意思是"匆忙、急促"。原指快速移动的动作，引申为时间紧迫时手忙脚乱的状态。last-minute rush特指"截止期限前的忙乱状态"。