It's never directly stated in the series that Suzanne competed in the Miss America Pageant. Most episodes talk about her being Miss.Georgia. However, in this episode she states that she's been to Atlantic City to compete in a pageant. The only pageant that is held in Atlantic City is the Miss America Pageant thus confirming Suzanne's participation in it.
Establishing shots show Suzanne, Charlene and Anthony gambling at Harrah's Hotel and Casino located on the Atlantic City marina.