I see pets serving two purposes. One mental health, they give you something to take care of and care for. This helps with your mental state.

Two, as guards and hunters / attack creatures. Having a nice pack of dogs following you as you explore will be an advantage, they hear and smell better than humans. Of course I use a Dog as an example.

Pets that are smart and willing to be with you would also be good. A creature that knows the world you are on, might alert you to dangers you do not know about.