If you check It with your luggage and it isn't properly bagged and packaged and it happens to be raining or snowing itll get soaked and dirty with the luggage and possibly broken when its thrown around. Its a bad idea to do that.
Also as a mom of 4 kids with much flying experience, 23 months is very old to be holding a kid on your lap unless its a very short flight. At that age they don't understand they need to stay in your lap and do MUCH better in their own car seat in their own seat on a plane.