Hi Dana,
Jamie has a great idea. Just one suggestion - if I have learned nothing else from 10+ years in tax consulting, always do your research and know what you are talking about before you call. The person you reach may not be a specialist, they might be new to the department, they may not understand the law themselves - you get the picture. Don't assume the person you are going to talk to is a specialist in the subject of your question. Always do the ground work and figure out what you think the answer is before you call, and why you think your answer is correct.
I took a look at the information for street vendors for DC and I don't think participating in a random craft fair meets the definition or the intent of the law. This looks like someone who is actually in the business of 'street vending' - generally, they have a single specific location where they operate from on a regular basis. Here is a couple of pages for you to look at:
http://dc.gov/DC/DCRA/For+Business/Apply+for+a+Business+Licensehttp://dc.gov/DC/DCRA/For+Business/Apply+for+a+Business+License/A+Directory+of+All+Basic+Business+Li...You are registering to collect sales tax in DC, not set up shop. Make sure the person you talk to knows this. Before you call, try to anticipate what questions the person might ask you and have your answers written down.
Good luck and let us know how things work out for you.