Tink (who is 11) has never been a big "tail wagger". The only time she does wag is when I come home and she is super super happy. Other than that, she doesn't move it much. (I do have to say, her docked tail is SUPER tiny - less than a 1/2 inch I do not think it was docked properly so I don't know if she doesn't wag because it takes a lot of effort?), she will wag it when I talk to her and get her all excited, which she likes to answer me in her "Tink barks"
Happy to read about your new baby!