Upvote:3
I don't think there is any legal issue with having no driver/guide as I know it is a popular place for Motorcyclists thanks to The Long Way Round. The Mongol Rally also travels there from London and it doesn't require any driver or guides for that section.
Here is a Link to the Lonely Planet Guide on traveling in Mongolia
http://www.lonelyplanet.com/mongolia/transport/getting-around
Here is also a link to the Mongol Rally page. You could try sending them an email to clarify the legality of traveling without a guide.