Sorry, "I breakfast" or "I am having breakfast". Is it really "I am at breakfast"? I understand that this is the literal translation but does it work?
It's really I am at breakfast, the 'la' in this instance has changed to fit the context.
Joe89 is right: 'la' here is a preposition meaning at, and also precludes 'micul dejun' from being a direct object. It definitely means I am at breakfast.
Here's my problem with this, and practically every sentence we hear with 'sunt': there is a distinct vowel sound after 'sunt', like SUNTuh, which is NOT a noise I have heard any native Romanian make. Some beta flaw in the recording?
True, the sunt pronunciation shouldn't have that sound after.