Hello: Like your Doctor said,
scars like that ( small, for scratch, without skin elevations) go away by itself , maximum, in children , it can take some time, 8- 12 weeks, the pink color become progressively in the color of her face, you can use to help a medication you can find over the counter in USA,
Hydrocortisone 1 % ( cream) twice a day for 2 weeks, and
Cetaphil ( moisturizing lotion) on a daily bases after the shower, avoid sun exposition after Hydrocortisone application, Hydrocortisone is a low potency
steroid, than can be used for a short period of time, without problems, if after 2 weeks with the cream the scar has not gone my recommendation is to see a
Dermatologist, Best wishes