Believe it or not, I was JUST reading about hiccups in young children. You didn't say how old your DD is so I'm not sure but....
Hiccuping happens when their diaphram(sp?) gets irritated. Babies hiccup alot because full tummies are capable pushing on the diaphram and that causes the hiccups. I would assume that a full on belly laugh could irritate it also. The article I read said that once the child gets older, there is more space in the chest cavity and this is less of a problem. Maybe it's that?