The driver takes approximately 1 second to get on the brakes from the point the woman starts turning to the crossing, knowing she's going to the crossing makes it easier, it's about 0.5s from being clear she'll cross the road to actually braking, which is a reaction reasonable time frame. It then takes the car about 1.5 seconds to slow down to walking pace, I think the driver wasn't hard on the brakes.
Having watched that many times carefully, the mistake the driver made was to brake! Had they not braked but committed to an avoidance manoeuvre, moving completely into the opposing lane, rather than it being an after thought then they would have been no where near the woman & child. Our driver training in the UK is absolutely awful when it comes to collision avoidance, about the only advice is 'brake hard' which often is the wrong answer, most of the time it's radically change your road position. This by creating more space removes the need to brake in the first place.
The main instigator of this incident was the woman pedestrian who didn't check to see if the road was clear but just walked out giving the driver very few clues as to what she was about to do until the situation became very tight.