WOW! Goontz's quick edit of the first shot revealed a really cute, adorable photo that I couldn't really appreciate in the first rendition of the shot!
As far as not cropping off body parts...well, yes and no. The way your first shot is composed is a type of composition I learned in design classes at university was called the "as in a painting" style of composition, where the subject literally touches three or four sides of the frame. As such, the way you framed it falls into that category.
The blown-out sky is a bit disturbing, but one could convert the picture to monochrome I suppose, and have it look adorable. I like the third shot somewhat. In years to come, these will become treasured family memories!