Children are generally innocent bystanders in violent crimes, and while the life of an adult should not be taken as less valuable than that of a child, the sentencing should be more harsh for the homicide of a child. Children often do not have the means or the knowledge to defend themselves and are therefore far more vulnerable. Someone taking advantage of that should be punished severely.
Ultimately, children make mistakes when they are young. Sometimes these mistakes have deadly consequences. It would take two lives to say to the guilty child that they had nothing redeemable left to ever offer society. That child should pay a penalty, but at some point it should end and the child should be given another chance.
No, homicides involving children should not require harsher sentencing. A homicide is just a homicide--one individual causing the death of another in an illegal manner. All murders should be punished equally, regardless of who the victim is. The only reason for degrees of harshness is the intent behind the murder.
If you murder someone, you should be punished. It should not matter who it is. If you intentionally kill someone for no reason other than your own anger, hatred, or grudges, then it shouldn't matter the age of the victim. A murderer is a murderer, no matter who they kill.