I am not aware that there is a "literary" term for what your describe, but the most common word is precognition. My dictionary defines it as "Knowledge in advance of its occurrence." My thesaurus offers a number of synonyms, including ESP, extra sensory perception, foreknowledge, premonition, and second sight; but precognition seems the best word to answer your question.
Emily Dickinson displayed a strong interest in death and wrote many poems on the subject. If she is speaking of experiencing her own death in her Poem 591 as you describe it, I would tend to classify that as a form of "poetic license" or a "poetic conceit."