Dear unsure--Relax and Enjoy,we have been cruising for over 55 years now , for myself since age 7, there have been many play companions and many happy children's hours spent aboard.
We have traveled with babies and growing children in many oceanview (i.e.-no balcony cabins) staterooms without tubs.
There has never been any kind of a problem,we all were kept busy--relaxing! The most difficult time in my life was 13 months between cruises (I am retired USAF)!
Just relax and enjoy- once you do it you'll have trouble thinking of any other kind of a vacation!