a "pool" of quadrille is the complete number of people needed to dance the quadrille, which is 8 (four pairs of people). A quadrille is a square dance. A "pool" in this context means a "group."

It sounds as if this sentence comes from an old fashioned novel. The lady wanted him to be in her quadrille set so that she could dance with him.

Here is an example of a 19th century quadrille dance http://www.youtube.com/watch?v=syiClqV1HBQ&feature=fvwrel