I have mostly sailed the classic ships, and find the dining rooms can be loud - sometimes loud enough that I have problems hearing the servers or the person next to/across from me. There are a lot of people in a small amount of space, and they're all talking. I don't know that a private table will help that much, as the tables are often very close together with little spacing between them - so while you may only have your party at your table, she could be close to a number of other of people at other tables. You may be better off requesting a quiet table (perhaps with a note as to why) - which may or may not include additional cruisers, depending on the dining room layout that cruise.
Something else I'd recommend in your case would be to go to the dining change location listed on the navigator when you board, and speak with the head waiter. Explain your concern and make sure the table in all the dining rooms will work for your party. They will be best able to know where your table will be located (and we've had corner/edge table numbers in one restaurant be right in the middle of the dining room in others) and be able to move you if necessary to ensure your family has a great dining experience.