DR Druxy, introducing a new cat to Annie could be more complicated than introducing a new dog to the dogs. You are wise to wait until after the move, which could solve the problem. I have found moving sometimes changes a few habits.
We have moved multiple cats around the country.
My first tip, NEVER open the car door unless the cat is in the carrier. I assure you that was not a fun activity with 4 cats in the car.
How is Annie in the car? Maybe you can take her for short rides to let her know the car doesn't mean going to the vet. On the whole, most of our cats did fine. Many cried the first hour or several hours & then were fine. Many were fine right from the start. Two of our cats needed mild tranquilizers the first day (test the dosage at home if you think it is needed). We made sure there was plenty of water for them to drink during the trip, & that the two nervous cats drank it so they didn’t become dehydrated.
While the doors were shut & the car was moving we let the cats out of their carriers. You might want to microchip Annie and/or put a collar with a tag on her.
Oh, don’t forget to take all the pet & people medical records.