let me get this straight....you dropped a carrot down your AC vent, right? ok, so i guess you mean a supply vent located on the floor, right? in the words of plato, that don't make no sense. unscrew the register and see if you can fish it out. HOWEVER, if i understand your issue correctly, the carrot is cool, so to speak.
did you hear the one about the gay guy that got a carrot stuck up his....lol just kidding.
it's not an issue. the carrot will just sit there and get eaten by rodents/bugs or rot. no biggie