The Miniature American Shepherd is in the AKC Herding Group.
Finding An AKC Show
Use the AKC Event and Awards Search page. There are search tabs for Conformation, Open Show Conformation, 4-6 Month Beginner Puppy, and the Companion Events (Obedience, Agility, AKC Rally®).
Or visit the AKC page of links to Licensed Superintendents. Each one has a website you can search for upcoming events and many allow online entry.
The AKC website also has great resources for anyone looking to get started in a specific event: