I’d always support the head in case they jerk and toss back.. it can happen.. but I’m old school (late 40s) and I’d still put formula milk in the fridgeI didn't see anything wrong with how she was holding the baby? If he was laid horizontal in her arms then yes, support his head but how she is holding him seems fine? I've held numerous babies like that and done no harm. Unless I'm to chilled out?