In reply to Jus: Camp used to make a helmet which was for climbing cycling and kayaking. Sorry cannot remember the name, I do recall it claimed to have the relevant safety certifications for all three disciplines.
In reply to Jus:
The shape of the head rather than size changes as you age.
Kids have a rounder head I think.
Take her in to try some onto check it stays in place as she looks up , Bunnyhops the curb etc.
Kong's "Scarab" is EN-rated for climbing, cycling (and other sports).
Petzl's "Meteor III +" is also EN-rated for climbing, cycling (and other sports).
Having said that, neither is a kids helmet and both have been designed with rock climbing in mind. There may be other multi-purpose helmets I'm not aware of.
Tough one. If it were for an adult I would definitely advise either helmet. Being for a 6 year old kid (I'm a dad too) I'd probably buy a dedicated cycling helmet and a climbing one looking for the "perfect" fit (they all have a size range) as this plays a fundamental role in the overall safety of the helmet. It may be an adult or kids helmet, it doesn't really matter, but it has to fit properly. My two cents.