When to offer support?

In the local news there is a story floating around that an older brother accidentally shot and killed his younger brother. Honestly I don't know if this is completely true or not. The one fact that I do know is true is that a 13 year old died this week and another family is suffering and in unimaginable pain. My husband asked me if I thought we should go to the family and offer any help right now. I said "No" but this is why--

This family is deciding where to have a funeral
This family is picking out clothes for their son to be buried in
This family is deciding on songs to be sung during the service
This family is trying to figure out where to have a dinner after the funeral
This family is selecting a place to bury their son
This family is figuring out how to pay for all this
This family is still numb with grief and shock
This family is putting on a "face" for family members coming in
This family is going through a hell that few people (including myself) can possibly understand- if the stories are true
This family is going through hell regardless because their child is gone

When to offer help? When to go to the families and offer support and some sort of comfort?

When the numbing effect of grief wears off (which unbelievably it does)
When the grief gets worse about 3-6 months after the death of their child
When the friends begin to back away because they don't want to "catch it" (death)
When family members become harsh and tell them "to get over it"
When people quit calling and asking how they are doing
When people only want to hear "Fine" when they are asked how they are
When people quit speaking their child's name because they don't want to make the family sad
When the family members no longer think they can live without their child anymore
When the family's pain is so strong they can only think to end their own lives and stop the pain
When the family is dieing it's own slow death while the world is moving around them

Right now this family is busy, right now they are surrounded by people and things to do. But soon, the house will become quiet and the pain will become worse. Soon when the world outside has forgotten their pain they will need their family and friends more than ever. Just because time continues to go by the pain does not get easier. The pain only gets easier to manage after years of practice. This family and all families need support beyond the "initial allowed grieving period the world allows."