Just outside of Bryce Canyon National Park is a Utah state park called Red Canyon.
The hoodoos aren’t as dramatic as they are in Bryce Canyon. However, the landscape is still striking and has the advantage of being dog friendly. In fact most, if not all, of Utah’s state parks are dog friendly.
From the visitor’s center you can start a 5 mile loop hike along Golden Wall which will drop you into the campground. Much of the hike is exposed so in the summer have plenty of water for you and your furry friends.