As I understand, he wish that then click on the thumbnail of a dog in gallery will be opened a page about that dog.
I don't think that is possible from the gallery. For that is intended the WP Gallery - to show more images as thumbnails, then on click to enlarge the images to see the details.
For what you wish the easy way is to make a table and in each cell put a picture linked to the intended page. Will look like a gallery but will be more like a menu. See at http://www.lustre-covoare.ro/produse/covoare/lana/
such a menu and when you click on any of the image from there will be opened pages with real galeries on them.