this purplish patch should be evaluated as it may be a sign of what we call as late Hemorrhagic disease of new though (late HDN), please don't get confused with the name as it does affect in later infancy though rarely around this age.
please see if there is any other site she has developed this kind of patch, as it develops at many places subsequently.
get a blood work done like (PT, aPTT
, CBC etc and if found abnormal only a shot of vitamin K will suffice. it will also rule out any other illness related to bleeding or hematoma
if every thing comes out to be normal you can be at ease.
hope my answer guides you,
wish your baby good health
Dr. Amit Kumar