It appears that thus far the youngest pilots to fly around the world are
Dan Dominguez and Chris Wall, who were both 22 years old at the time. See generally
this site, which should provide some ideas and inspiration.
Arguably, 11-year-old Tony Aliengena was the youngest person ever; but of course he had no license and was flying on his father's ticket (à la
Jessica Dubroff), which doesn't cut it IMHO.