If you are convicted of speeding while you hold a learner permit, you will not be able to

While you hold a learner permit, if you are convicted of a traffic violation that adds points to your driving record, you will not be eligible for a provisional license. You must hold the learner permit for 6 consecutive point-free months before you can apply for a provisional license. [Learner Permit Stage, GRAD Program Enforcements, Gradual Rearing of Adult Drivers (GRAD) Program, Types of Driver Licenses and Permits, District of Columbia Driving Manual]