Sometimes having a pet either as window dressing or as a character can enliven the person. How people treat animals does tell you a lot about them as well as their culture. Now when I am referring to pet, I am specifically referring to a non-sentient life form that lives with and cared for by a sentient life form.
So to write a pet character, you need to figure out: Species? Physical description? How are they treated? Do they have a job? Like any character, they need to serve a purpose in the story.
In Other Systems, there are a few pets mentioned. I will go in detail about Rockford.
Species and Physical Description: Rockford (Rocks) is a massive gray and white spotted domestic house cat. While dogs went extinct on Kipos, cats lived on due to their smaller size and independent nature especially aboard the Fleet.
Life Style: The humans on the Revelation consider him Diane’s cat in the sense that Diane wanted a cat, picked one up, now feeds, waters, cleans up his litter box.
However, Rockford considers The Revelation his domain and the crew his servants. He is benevolent. He gives preference to the Human called Diane who feeds, waters, and cleans up after him. He also gives preference to any Young Human as they tend to play with him. During the day, he wanders around the living quarters of the Revelation and pushes his scent glands on whoever is not working. While he does consider Diane’s bed a favorite resting spot, he also has his own cat-sized billet (Humans refer to it as a closet) with his toys and a scratching/climbing area and his litter box where he can retire until his special skill set is needed.
Employment: (No, they do not have a rodent problem.)
First of all, he is an excellent judge of character.
Secondly, when people are having a bad day and don’t want to deal with the hardship and the blackness of space, or just the annoyance of other human beings, Rockford is willing to cuddle while they watch vids. He also likes to play fetch with his stuffed fish and he likes to bat at pieces of fabric. He knows humans find it soothing when kitties purr.
Now you might not think this is an important job, but then you have never dealt with the black emptiness of space or a contained environment where you are stuck with the same people day after day.
Other ship’s cats in science fiction that make a huge difference in people’s lives…
When Ripley is about to blow up the ship on Alien, she hears Jonesy on the com system and rescues him. Why? She is emotionally distraught (as her crew has been killed or impregnated by the Alien) but rescuing the cat and taking care of him, calms her down and allows her to continue doing what she needed to do to escape.