At that moment, she felt free and didn't have a care in the world.

care 在这里是名词，意思是"忧虑、牵挂"，指让人操心或担忧的事情。 not have a care in the world 是固定表达，字面意思是"在这个世界上没有任何忧虑"，用来形容完全无忧无虑的状态。