Money Market Fund Parity Act of 2009 - Directs the Securities and Exchange Commission (SEC) to revise, according to specified requirements, rules relating to net capital, custody and use of customers' securities, and certain underwritings to provide for: (1) treatment of securities issued by qualified money market funds comparable with the treatment under those rules of other low-risk securities and deposits; and (2) the expanded use of securities issued by qualified money market funds for financing by brokers and dealers.