First of all, I would let her be in your room away from the dogs (like you said) for a couple weeks before you try anything with the dogs. When Kiba is used to her new surroundings, you can try putting her in a crate and then letting the dogs check out the crate and see what they do. You said Zeke hasn't tried to hurt her, but would Josie? Do either of them have a high prey drive?

I have a dog/cat mixed household and everything goes smoothly. Sometimes I'll get a cat who hates dogs, but after spending a few days around my dogs, they are fine. I'm not too worried about the cats who don't like dogs because they usually just steer clear anyway. I worry more about the dogs who don't like cats because they're obviously much bigger and could do harm.

Just use extreme caution and introduce them several times with the dogs on leash before you think about letting them off. Also keeping Kiba in the crate for the first several times is a good idea too. Based on their reactions, you can decide what your next step will be a lot easier.

Also, maybe you could bring Josie and Zeke to your mom's and see how they react to the cats there? That will probably help your decision on what to do.