So what can I eat for breakfast with no dairy, eggs or grains?

First, focus on what you can have and not what you can't have. It'll make things easier!

Things I made then, and still often make:
Hash browns (grate potatoes and season, I like Cajun and salt for seasoning).
Leftovers! Remember, it doesn't have to be true breakfast foods.
Fruit.
Rice chex with rice milk.
Dice or sliced potatoes.

Truly, if you can get out of the mindset of breakfast foods, you'll soon get in a rhythm and be fine. :)