Before I begin, I have absolutely no intention of getting a cat, but I have always wanted to foster cats. My dog is a stray mutt we adopted after people nearby threatened the woman who was feeding his mother to get them out of there. We have no idea what his genetic composition is, who the father is but he is most definitely a mixed breed (various breeds, is my guess). The mother is a mutt too.

So how does one go about determining whether a cat would be suitable in the household? What signs are there? My dog has never been near a cat, but I feel like he has hunting tendencies (he runs after birds, though I am not sure if he wants to play with them or kill them as he runs after dogs who he is friends with too). He is good with small puppies, small dogs, children, even babies (idk if that is even relevant). He's 9 months old, medium sized so obviously I can't take him near a cat to 'experiment'. Just curious though. Any help would be greatly appreciated :)

Puppy tax - https://imgur.com/a/IVPtnxH [if anyone wants to guess his breed(s)]