Help!! My easter cookies lose their shape when I bake them!?

I am making some cookie cutter cookies for easter, but they lose their shape after I bake them! My bunnies and eggs are turning into golden-brown blobs instead of the cute little shapes that I wanted.
Am I doing anything wrong? How are people able to make those cute little holiday cookies??
Do you think it would help to use actual butter instead of margarine, as well?