Princess cruises is great for all ages and they definitely do not cater to seniors only. There are many honeymooners and families onboard depending on the time of year. It is a more subdued line than Carnival, but we are a family of 5 and have never felt like the only youngsters onboard! My three teens just love Princess too.
In November, on most cruiselines, you will see an older clientele. During summers and school vacations you will see more families.
Princess does run some great specials so it would be worth it to check them out.