Judaism, like every religion, has strict laws about burial after death. The short, short version: no cremation, nor really any kind of physical disfigurement (for instance, removal of organs) is permitted. The body is thoroughly cleaned, dressed plainly in white, placed in a simple wood box, and lowered into the ground as soon as possible following the person's death. Then a period of mourning, known as sitting shiva, begins.
Dorothy Parker (formerly Rothschild) was born to a Jewish father and Protestant mother, though her mother died when she was young and Dorothy apparently detested her father. Dorothy grew up to be a poet, a humorist, a magazine editor, a professional celebrity, and really just an amazing, inspiring, creative human being. She wasn't raised Jewish — she attended Roman Catholic elementary school, though she wasn't really Christian either — and spent most of her life trying to conceal her Jewish identity, rather than embrace it.
While we might like to theorize, we cannot say whether accepting her Hebrew heritage would have helped Dorothy to happier marriages, or kept her from her disastrously deep bouts of depression, or from her drug abuse and alcoholism. Judaism does not equal happiness. (Yeah. No kidding.)
What we can say for certain, however, is that had Dorothy accepted her Judaism her earthly remains definitely would not have ended up stashed in an urn in someone's file cabinet and forgotten for twenty years, which is what ended up happening.
So, we don't feel too presumptuous in saying that she might have been at least a little better off.