I remembered running across this:
My goal time is a little longer than the current women's "speed record." The AT Conference doesn't like to keep speed records, but they told me the fastest woman they're aware of did it in 103 days, which is just over three months.
From: http://runtrails.net/journal/prep_2.htm
Which is an account of a woman ultra-runner's supported journey on the AT. You might contact her (Sue Norwood) or the ATC for more details.
Good luck,
-adam