The Brass Ring
by Nancy Tafuri (1996)

For ages 2 and up, this illustrated book features Watch Hill's Flying Horse Carousel.
From www.nancytafuri.com:
Nancy Tafuri's young protagonist is on vacation and exulting in her first taste of independence. Now that she is 'Big' she can swim, explore, and make new friends. But, she decides, what she likes best is the carousel. She has bought her own ticket. The brass ring is in the slot. Thunder, her favorite horse, is waiting. The music is starting. And what a ride it is!