In the original thread on the old site, DadsDream posted (with links) about its origin in the old Southern Minstral shows ("Who dat say who dat when I say who dat") and others posted about use in pre-'70s high school games and then college games. I seriously doubt that the Bengals can pre-date that.
That doesn't answer the real question, though. The question isn't which phrase originated first, it was which was used as a football chant for their respective team.
I say we put it all on the line this weekend. Whoever loses this game forfeits the right to us that phraseology anymore...until after the next game between these two teams.