Naming Ionic Compounds with Transition Metals
As stated in the Wikipedia article for iron:

Like other group 8 elements, iron exists in a wide range of oxidation states, −2 to +6, although +2 and +3 are the most common.

Thus, assigning $\ce{FeO2}$ as an iron(IV) compound is not something that is impossible, but it is unlikely. There are only a few compounds with that are iron(IV).
A more likely scenario is that $\ce{FeO2}$ may contain other anions of oxygen:

Oxide $\ce{O^2-}$
Superoxide $\ce{O2^-}$
Peroxide $\ce{O2^2-}$
Ozonide $\ce{O3^-}$

While oxide is the most common anion, there is another on the list above that is reasonably common. Which is it? If you have that anion, what is your oxidation number for iron?