The "at" can stay. It sounds more formal, but there's nothing wrong with that. I think the first sentence is more common and probably more what you mean to say, but the second sentence is kind of charming. When it comes to meals, at least in American English, "take" is used most often with tea. If it's used with a meal that isn't tea, the meal is probably fancy and someone is bringing the food to you. Like, if you were staying at a very nice hotel, you could take breakfast in your room at 8:00. Or if you could afford a personal chef, you could take breakfast on the patio when the weather is nice.

I wanna say that the word breakfast is used with have as the meaning to eat

seems they don't "take" breaskfast. they only "take" medicine :)

i like that second answer...great explanation...i also exploit it, thanks. i think no need to more answer.

What time do you have (eat) breakfast? Drop the 'at', not needed. What time do you have breakfast usually? What time DID you have breakfast?