Pets in stories can be used not just as symbols, cannon fodder, or heartstring pulls but also as character cues or major characters in their own right.
Off the top of my head I can think of:
Heinlein's DOOR INTO SUMMER prominently features the protagonist's cat, Petronius (Pete) who is clearly a better judge of character than the hero. The cat faces peril, gets a few good licks in, and gets you rooting for him. Plus he gives the story its title.
Dickson's TIME STORM features a traumatized leopard that attaches itself, housecat-like, to the monomaniacal protagonist and an equally traumatized girl, both of which provide the crazed protagonist with dependents that ground him in the chaotic fractured universe of the story and ultimately get him to appreciate the extent of his insane quest.
Heinlein's entire THE STAR BEAST revolves around a young adult's effort to protect his inherited alien pet who turns out to have a "hobby" of its own. (Besides eating used cars.)