First-Time Homebuyer Credit Continuation Act of 2009 - Amends Internal Revenue Code provisions relating to the first-time homebuyer tax credit to: (1) extend such credit and its waiver of recapture provisions through November 30, 2010; (2) extend through December 31, 2009, the election to treat, for tax purposes, a residence purchased in 2009 as having been purchased on December 31, 2008; (3) allow taxpayers to treat, for tax purposes, a residence purchased after December 31, 2009, and before December 1, 2010, as having been purchased on December 31, 2009; and (4) extend through December 31, 2009, the coordination of the first-time homebuyer tax credit for District of Columbia residents.