This is an interesting idea, even though doing so is currently illegal:
I don’t know what sort of special care a quoll might require and how that might differ from caring for a ferret or a cat.
And if you want a dog, then you could get a dingo. Some dingoes do tame down quite nicely. A few have even made it as stockdogs, and at least one has made as a guide dog.
Not all dingoes make good pets, but they are closer to a domesticated animal that those marsupial carnivores, which might require some really intense selective breeding to make a safe family pet.
