Normally I would mention Arlington/Fairfax, but its full. Might want to consider the Loudoun County Chapter of the Izaak Walton League of America (IWLA). Great programs and alot of fun. IWLA Youth Programs
One of the Fairfax members does teach a kids league and there are opportunites at the NRA range for kids.
Here is a list of IDPA for VA: IPDA - VA
Hope this helps!
ETA: Vafish is the one!