First appearance: Military Comics #1 (August 1941), published by Quality Comics.
By the way, Military Comics #1 was also the issue that introduced Blackhawk.
Joan had a feature in Military Comics that lasted for seven issues, her final Golden Age appearance was cover-dated February 1942.
It wouldn't be until 1943 that Timely Comics (the predecessor of today's Marvel Comics) would introduce their own "Miss America":
from Marvel Mystery Comics #49 (November 1943)
However, the Quality Comics character didn't appear until about 20 years after the first Miss America pageant/competition.