Quicker Veterans Benefits Delivery Act of 2013 - Prohibits the Secretary of Veterans Affairs (VA), during the six-year period after the enactment of this Act, from requesting a medical examination in connection with a claim for veterans' disability compensation when the claimant submits medical evidence provided by a non-VA medical professional that is competent, credible, probative, and otherwise adequate for making a claim decision.

Requires the Secretary, during the same period: (1) to assign a prestabilization disability rating of total, 50%, or 30%, as appropriate; (2) to provide temporary minimum disability ratings for veterans not assigned a permanent rating; and (3) to not count any veteran assigned a prestabilization or temporary minimum rating under any backlog of unassigned ratings.

Authorizes the Secretary, during the same period, to certify benefit payments by mail or account deposit before the first day of the month for which such payments are due.