I moved in on Monday, but I left the cat at the old place until Tuesday, which allowed me to get the new room sorted out. When I brought the cat in, the dog immediately went over to her carrier to check it out. Again, it was more of a curious thing, not a defensive "I must fight this invader" thing. The cat was thoroughly freaked out though and when I got her in my room, she hid in the closet and started panting pretty heavily.
Since then, she's calmed down quite a bit and has grown comfortable in the room. It helps that the room is upstairs and far away from where the dog hangs out downstairs. She's eating and going to the bathroom normally which is very good.
Last night, I actually carried the cat downstairs and held her while the dog came over. That didn't last long as the cat tried to bury her head into my neck, but once I brought her back upstairs, she calmed down very quickly and started purring again once I petted her, none of the panting from the first time.
So she at least recognizes that my room is her safe zone, but it will still take some time until she's comfortable around the dog.