I think you can make any situation work. The cat is a great idea!
They can keep each other company. The older dog is also good because a puppy really does need 24/7 attention. I think you are doing things right. It would also be great if you could find a neighbor or hire a professional pet sitter to ocme in once a day and walk and play with her for an hour.
You are going to be a wonderful mommy to your new fur baby!!
