You could try a SlimCat food dispenser ball - you put food inside, adjust the holes so they just barely let the food fit out (be sure to read the instructions, the Amazon reviews sound like lots of people didn't figure out how to do this), then let your cat push it around the floor & pick up & eat the food bits as they fall out. I got one at my vet's (but rarely use it because I normally feed canned food) but they're cheaper, of course, on Amazon. Obviously you could really only do this in a room with a hard floor - dry cat food is kind of greasy. It was fine on my hardwood.
But the dog does complicate things. Can you put up a baby gate that the cat can get through (over or under) and the dog can't, and put the cat's food in the room the dog is closed off from? I do this when family visits with their dogs.