I conducted a funeral for a baby who died from cot death at 12 weeks. I still think of it, and the family... seeing the father carrying in that tiny white coffin... :(
It was one of the hardest days of my life, keeping it together & being professional, so I cannot begin to imagine how the parents felt. After the burial, I got into the car and sobbed, feeling lucky that my part was over & just wanting to get home to my own child, and get my hand inside his vest, to feel his skin and warmth.
You sound like a lovely friend, just remember your friend... in my experience people tend to forget you after the funeral & in the weeks that follow, when ironically you feel worse, as the numbness & shock has worn off, and the reality and loss sinks in.
to those who have lost children. I saw a post on Facebook about people who lose their parents are called orphans, you lose your husband & you're a widow, but there is no term for those who lose a child, which must be the hardest loss of all.