Work is defined as a force moving through a distance. Force in this case is the weight of the child being lifted = mg.
So the work done by the woman is mgh
35 kg * 9.81 m/s/s * 1.5 m = 515.025 J of work is done by the woman in lifting the child.
The child is doing no work while being lifted but does gain 515.025 J of potential energy because of the work done by the woman on the child.
Note that the woman does no additonal work in carrying the child forward 6.5 m.