It all went down in Jersey last September -- 16-year-old Nia Drummond flunked her "Idol" audition ... and as she made her exit, accidentally tripped and fell down a flight of stairs ... an embarrassing accident that aired on "Idol" last week for millions to see.

We're told Drummond was taken to a nearby hospital immediately after the nosedive -- where she was treated for a sprained ankle.

Thankfully, she's all better now. See you next fall!