Hey Kinderchicklets!
Good question, but actually you asked two questions there. The first is what is "is Princess eating pebbles" and mostly the answer is no. She's moving the pebbles around to clean up and remake her nest. Because they don't make a nest like a robin or a goose (you wanted Mother Goose in Edmonton, remember her nest?) instead they make a little bowl shape hollow in the gravel to hold their eggs during incubation and the chicks when they are very small. But everytime they get off and then get back on the eggs/chicks, they move the gravel around and they need to fix it up. Imagine if tomorrow morning you didn't make your bed and when you went to bed tomorrow night you couldn't move your sheets at all, you could only lie on top of them ... would you be able to sleep comfortably? But if you had made your bed in the morning, when you went to bed, your bedclothes would be all lumpy and bumpy and you would be able to sleep comfortably, no problem.
Your second question is "does Princess eat pebbles" and the answer is yes, sometimes. Peregrines don't have teeth like we do, so they eat a few pebbles, store them in their gizzard and use them like teeth to grind up their food. Now a gizzard is like a pouch in your neck - it would be below your chin but above your bellybutton. If you were one of the peregrine chicks you wouldn't need any pebbles because you are still very little and Princess and Ivy feed you only little pieces of food. But if you were Princess or Ivy (or if you were an older peregrine chick) you would eat some pebbles and they would sit in your gizzard and then when you ate food the pebbles would grind up your food, like your Mummy's blender at home.