Within Bryce Canyon National Park, pets are permitted only on all paved surfaces: campgrounds, parking lots, paved viewpoint areas, etc. Pets must be on a leash and cannot be left unattended or tied to an object. For more info please visit The National Parks guide on pets in Bryce Canyon.
Pets are allowed on the trails in Red Canyon and Dixie National Forest, as well as in the Grand Staircase-Escalante National Monument. If you have any further questions about pet regulations, please visit the nearest visitor center for additional information.
In Panguitch, there is a kennel for a safe and comfortable option for you to leave your pet. More information can be found here: Renting a Kennel.