Yes, there are four power berries that your dog can find for you. There are 10 specific locations where the berries might be. The dog can find other things, like mushrooms, truffles etc, in those places, too.
To find these things, take you dog to one of the spots and play the "search" command until the dog stops in one place and barks. The dog will then dig up whatever is there and you'll be able to pick it up.
The special spots to search are:
1) To the left of the flower bed by Lyla's store
2) The mound of earth in front of Ronald's store between the two trees
3) Bar/Tea Shop by the tree near the northern part of that area
4) Near the two trees in the middle of the Goddess Spring area
5) The tree at the top right of the stairs to Clove Villa
6) Near the stairs in the center of the area in front of Woody's shop
7) Near the righthand set of stairs in front of Woody's shop

In the very center of the Pike Mountain area
9) Same area as 8, but at the top of the stairs (doesn't say which one)
10) To the left of the Flower/Tool Shop sign in the Plaza area
ERG Beaten