Belated thanks for the responses.
We've climbed to refuge Orisson at an easy pace and taking as many stops as required. We were there before noon. So, it's perfectly doable. The next day we took a taxi up the road, up to Croix Thibaud (where the chemin leaves the paved road) and walked on from there.
On the whole, we've found that it's boredom rather than fatigue that slows down kids. Bring a little toy, or tell a story, and the distance will be covered. Our max stage with the child was Roncesvalles to Zubiri (over 20km). 13-15km is more reasonable.