Gale already has a cat, albeit winged, so cat it is.
Shadowheart I feel is also a cat person. Something less emotionally needy that she can still cuddle when she needs to.
Lae'zel would have a snake. She'd respect its predatory nature and find its cold lack of empathy something to admire.
Wyll I feel would have a dog because dogs are the pet option of heroes, and while he'd take decent care of it he wouldn't really love the dog the way he should.
Astarion... Would probably hate every sort of pet you can get. They all need maintenance of some sort and he'd see that as boring responsibility.
Maybe Astarion gets a pet rock or some sea monkeys.
