The Dog Crate is where you raise your Puppies and breed your adult Dogs. You’ll find it in the list of blueprints. It is crafted in two stages. Resources for construction can be found in the game on your own or can be purchased in the game store 

It is also where you can assign specific pets to either walk around your base or accompany you on your adventures.  
You can find more on how to take dogs with you to other locations here: link.