I'm an American that has lived in Buenos Aires for the past year and a half. I can tell you that self-employed people in Argentina are called monotribuistas. AFIP, the Argentina agency in charge of customs and taxes, recently made changes to all of the rules regarding being a monotributo. You can read an articles about this, in Spanish, in La Nacion under the "Monotributo" tag.
I have an Argentine DNI, though I have one because I'm in a graduate program here. While I can't tell you the paperwork that would be required in your specific case, I would suggest that you contact Celano & Asociados. They are an Argentine law firm that specializes in helping foreigners with Argentine immigration issues. I also have a friend that is an Argentine accountant. If you are interested, I put you in contact with them.