She's been Minerva since a 1942 comic strip.
It doesn't make me feel that differently about her -- but her origin is slightly surprising. She was designed to be a substitute bunny. Mickey was replacing the randy Oswald the Rabbit, so he needed a skirt to chase. Minnie was the skirt -- from the very first Mickey Mouse cartoon:
Minnie, who at the time was not yet named, was designed in the fashion of a "flapper" girl. She was so probably intended to follow the trends of then-modern youth culture in an effort to add to her audience appeal.
Mickey and Minnie debuted together in Plane Crazy, first released on May 15, 1928. Minnie is invited to join Mickey in the first flight of his aircraft. She accepts the invitation but not his request for a kiss in mid-flight. Mickey eventually forces Minnie into a kiss but this only results in her parachuting out of the plane.