No, the right to guns is in the US constitution. Washington, DC is part of the United States and must abide by the constitution just like everywhere else in the US. The fact that it is the capital doesn't mean it can go against the rules. In fact, it should lead the way in upholding the constitution and in equality.
If the law of the land is that handguns cannot be banned, why should that be any different in the capital? Do politicians feel that they should live in a safer city than the rest of the country? Of course, if voters in that district decide to ban handguns, that is their decision so long as it is considered constitutional by the courts. But just because it is the nation's capital doesn't mean that handguns should be banned there.