I would get her out of that carrier now. It is making him feel trapped and he is going to be stressed and stay on high alert. Instead, I would find a room with a door and put the new cat there. With a litter box, scratching post, food, water, and a place to hide. Cats need to develop a sense of safety before they can welcome others. That requires them to have their own territory. If you give them a room like that, it may take a few days for the kitty to feel established and come out and interact with you.
It will take time.
Once that happens though, open the door a crack and let the dog and cat sniff each other. If they back off, let them. If they hiss growl, close the door and try again in an hour. Or three. Put treats by the door when you try a second or a third time, so they associate the other creature's scent with pleasure. Keep doing this for a few days.
It may take a week for a cat to accept a dog. But if you go slow like this, they will really have a good chance to develop a friendship and accept each other.