I guess I'm fortunate that I can eat small amounts of carb at breakfast, as long as it's no more than about 25 carbs.
Even so, my breakfasts are generally Carb Master yogurt (3 net carbs, available at Kroger, Food 4 Less or Ralphs), eggs 800 different ways, low carb bagel (Western Bagel makes one called "net 10" it has ten net carbs since it's very high in fiber) and/or a slice of Orowheat "light" wheat which has something like 4 net carbs after you deduct the fiber.
Some folks find that they do well with left over roast beef, chicken or sausage from the previous night's dinner. There's no hard and fast rule that you HAVE to eat so-called "breakfast food" at breakfast!
There is also a really terrific protein bar that I buy - they can be used for a snack or meal replacement - called "Oh Yeah Protein Wafer". Only 6 carbs a serving and they taste wonderful. You can find them here:
ISS Oh Yeah Protein Wafer Bars if you want to buy them by the box (I do - usually two boxes per order. They keep well) or here:
Search Results : LoCarbU.com if you just want to try a couple out first.