Veterans Retraining Act of 2009 - Authorizes the Secretary of Labor to pay to each covered veteran an assistance allowance for each month such veteran is enrolled in an employment and training program that teaches a skill in demand, as determined the Secretary. Limits such assistance to six months for each 10-year period. Includes as a covered veteran one who is: (1) unemployed for at least four consecutive months before applying for such assistance; (2) able to successfully complete the program; and (3) ineligible for other veterans' education or training assistance. Authorizes payment of a stipend to a covered veteran for moving expenses related to the receipt of such training. Authorizes appropriations.