The Diary Review blog has several blog posts about European diaries from the 1500s and earlier, but none of the authors of these diaries were literary figures (although some of them published non-fiction). There is, of course, the famous "diary" of Philip Henslowe (that is, "famous" among scholars of English Renaissance drama), but this is really " collection of memoranda and notes that record payments to writers, box office takings, and lists of money lent" (Wikipedia) and not a diary in the usual sense of the word. In addition, Henslowe didn't write any literature.
The diary of Richard Torkington's pilgrimage to Jerusalem in 1517 was for some time believed to be the oldest diary in the English language; its first editor, William John Loftie, give it the title Ye Oldest Diarie of Englysshe Travell. The Pilgrim Libraries project has identified a number of older accounts of pilgrimages, usually written afterwards rather than during the voyage, and none of them by literary figures. In English, one of the most famous diaries is probably the one by Samuel Pepys, who was a civil servant and politician rather than an author of fiction.
The above paragraphs represent the results of my searches so far, which have been unsuccessful. I am looking for the earliest surviving diary by an author of poetry, drama, stories or novels, not treatises, translations or pamphlets. The author should primarily be known as an author of poetry, drama, stories or novels, ideally published (or circulated in manuscript form) during their lifetime, but since some people think that "primarily known as ..." is a matter of opinion (e.g. is X better known as a poet or a diarist?), this is only of secondary importance. I am curious to find out whether it says anything about the author's ideas about his craft.