It is advised that very young children not have rag quilts. They will suck on the fringe and sometimes fall asleep on the fringe ... and that could either cause aspiration of the left over threads in the fringe or smother them.
Flannel does a great job. Personally, I love pinwheels in vibrant colors.
Fleece with just one layer serged at the edge also is nice and quick. It's just not as pretty [to me.]