Safety is my first priority at every session. This is especially important for newborn, baby and child photography. I never sacrifice the safety of a child for a shot. Often clients select a photographer based on price, rather than their experience with photographing children. Be sure to do your research and be sure that whoever is photographing your child has the knowledge and experience to do so safely! Also know that many shots you see posted on sites like Pinterest and Facebook that look dangerous are usually (hopefully!) composites.
Here is a recent example of how I put safety first. This little boy was a fairly good sitter. However, it was a hard surface and he was a little unsteady. Mom was right next to him the entire time to spot him. She was always within arms reach as you can see below.
The image on the left is the original image. Mom's hands were not in most of these images in camera, but for the one on the left he began to lean and her hands were in the shot. I loved his expression, so I removed her hands in the right (final) image.