((hugs)) I know it's frustrating, but that list isn't *that* bad! Yes, by all means keep offering!!! Give her the thing you KNOW she will eat, along with something else. Fruit...watermelon chunks, sliced grapes, cantelope.....if she would eat a bit of fruit, a bit of dry cereal, and a bit of yogurt, that really is a good breakfast.
Also...could you try mixing in a different kind of cereal with the cheerios? Just to get her used to some variety? Kashi makes a cereal called "Mighty Bites" that is super-healthy and really yummy. Maybe toss a few in with her cheerios....and then keep doing it....it takes many, many times for a lo to be offered something before they might try it. yhe first step? Get them used to seeing it.
HTH!