Harriet Quimby was widely celebrated for her flight over the English Channel, but didn't receive the fame she expected. It was a matter of bad timing; her flight occurred on the day after the sinking of the Titanic. April 16th was the day that newspapers throughout America and Europe printed the news of the tragedy, so Quimby's amazing feat quickly became second page news.
Despite her untimely death in July, 1912, Quimby inspired future female pilots like Bessie Coleman and Amelia Earhart. Bessie Coleman was the first African American woman to earn a pilot's license, in 1922. Amelia Earhart was the 16th American woman to earn her pilot's license in 1923. All three women are enshrined in the National Aviation Hall of Fame.
You can learn more about Quimby, Coleman, and Earhart on the website for the National Air and Space Museum. There is also a BrainPop that you can watch on Amelia Earhart.