In a perfect world, I would have waited until your old girl was gone before bringing in a puppy. As it is, if you put her down, because the puppy is coming, you will feel guilty. Of course, we humans ALWAYS feel guilty when we have to send our beloved pet to the bridge. In all honesty, if you feel it is time for your old girl to go, have her put to sleep. If you can find a vet to come to your home, I highly recommend it. That is what we did for my old girl.
If you opt to wait and your old girl is still here when the puppy comes - keep them separated. It would be very stressful for your senior to deal with a puppy. I would keep them in totally different parts of your home. I really feel for you. I wish you the best in this very difficult situation.