In the sentence "A. My family and I enjoy camping," the word "camping" is a gerund. In this context, it functions as a noun, representing the activity that the family enjoys.
In sentence B, "camping" is used as a present participle, describing the ongoing action. In sentence C, "camping" is also functioning as a noun but is part of a compound noun, "the camping club," and not as an activity enjoyed.
So, the correct answer is A.