keeping the new cat in a crate for a day would be pretty stressful for the cat. I'd keep him (or her) in a bathroom for a day or so. Zoe will be able to sniff the new addition under the door and start to become aquatinted with the cat. The cat will be able to get to know Zoe some this way too.

I have a baby gate on my bedroom door so the cats can get away from the dogs if they want. It's usually not a big deal though, my cats and dogs often lay and sleep together. It's when the dogs are playing and roughhousing that the cats usually retreat to the bedroom.

I'd also suggest keeping the cat and Zoe separated when no one is home, at least for awhile.

Cats and dogs can be funny. Usually people worry about dogs hurting cats but it's often the cat that beats up on the dog. At Christmas we took Nacey to my in-law's house where she met my sister-in-law's cat for the first time. Nacey couldn't have cared less about the cat, but the cat hated Nacey. The cat guarded her toys and food bowl from Nacey, she even jumped on Nacey at one point when Nacey got too close to "her room".