I scrambled them and served them to CC just the way they came out. Eggs seem to be a perfect finger food: soft enough for her to chew and swallow, but solid enough to form their own clumps and stay together when chubby little fingers grab and mash them.
CC liked them (she ate the whole egg, actually), but I learned that I should cook them differently. I stirred them constantly the whole time they were cooking, which made much smaller pieces than if I'd let them cook a while first before stirring them. Lesson learned; next time CC will have bigger and better pieces of egg.