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We found the answer to your question at The Word Detective, a treasure trove of etymological explanations written by syndicated columnist Evan Morris. Morris, in turn, says he discovered the origin of "John Doe" in a book called What's in a Name?, by Paul Dickson.
The phrase is older than you might think. "John Doe" dates from the reign of England's King Edward III (1312-1377). A famous legal document from this period labels a hypothetical landowner "John Doe," who leases land to a "Richard Roe," who then claims the land as his own and kicks out poor John.
The names don't have any particular relevance, other than the fact that a doe is a female deer, while a roe is a smaller species of deer. But the land dispute in question became a famous legal debate, and the names survived their circumstances.
The online legal dictionary FindLaw defines John Doe as a "party to legal proceedings (as a suspect) whose true name is unknown or withheld." The female equivalent is Jane Doe or Mary Major. A second male suspect is dubbed Richard Roe, and subsequent ones are referred to as John Stiles and Richard Miles.