In 1985 Tania Abei did it at age 18 (though I had thought she was younger but apparently not.) Her story was chronicled in Cruising World magazine and as I recall was fraught with "stuff" happening. She eventually wrote a book about her adventure, called "Maiden Voyage."

I think a really really gutsy, and able 18 yr old is pushing the envelope here. A 13 yr old? This sounds more like an adolescent's motto - "I want... I want."

Tania's articles were fascinating. Just reading them fulfilled my wanderlust. There is a LOT of ALONE time on a boat.... After the excitement wears off, and the first storm on the open ocean, I'd expect many potential round-the-world sailors to call it a day and limp home.

A 13 yr old? Sheesh. I'd have to say NO if it were my daughter.
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From Amazon - Reviews of "Maiden Voyage"
From Publishers Weekly
Challenged by her German-Swiss father, an 18-year-old New York City bicycle messenger in 1988 became the first American woman, and the youngest person, to sail alone around the world. In this jaunty account of her journey, she veers between the perils of solo sailing, her relationships with her separated parents and the death of her mysterious mother. Aebi, writing with freelancer Brennan, reveals her lack of sailing knowledge and experience, describes the heavy seas and weather she endured, her numerous problems with malfunctioning equipment, the countries, people and cats she encountered and a sympathetic French-Swiss whose boat sometimes accompanied her own. The story is so compelling that sailing enthusiasts will read avidly on to the triumphant finish. Literary Guild alternate; author tour.
Copyright 1989 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

From Library Journal
This is the story of an 18-year-old New York City girl and her exciting solo circumnavigation of the globe on a 26-foot sloop with only a cat for company. Aebi had little previous experience, so most of what she learned was "on the job" and from people she met en route. One of the most appealing aspects of this particular single-handed sailing account is Aebi's naivete and the caring response that she encountered all over the world. Her 27,000-mile, three-year trek is usually attempted only by practiced sailors, and her survival was achieved by pluck, inventiveness, helping hands, and a good deal of luck. Armchair sailors will cheer and dream a little and veterans may only shake their heads. Recommended.
- Susan Ebershoff-Coles, Indianapolis-Marion Cty.
Copyright 1989 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.