Is it impermissible, Islamically, for my sister to work as a graphic designer, given that she adheres to the full hijab, does not mix with men, and dedicates a portion of her salary to charity? And is her work considered undesirable even with her good intentions and her help to people?

There is no harm in your sister's work as a designer if she does not design forbidden things, such as forbidden images or advertisements for something forbidden, provided she adheres to the hijab and avoids mixing with men. In this case, what she earns is lawful. However, if she designs forbidden things, she is sinful and her earnings are unlawful.