Bit late in replying to this so may not be of use now, but a few ideas,
There is a nice pool in the centre - www.chamonix.com/piscine-du-centre-sportif-richard-bozon,spa-relaxation,48-3113-sitraLOI321531,en.html
A trip on the mountain train - no climbing or much walking - www.chamonix.com/montenvers,81,en.html
The crystal museum (which sounds rather boring but your DD may enjoy looking at the 'pretty' stones and colours, mine DS did when younger, now he likes to look at how they were formed etc) - www.chamonix.com/musee-des-cristaux-espace-tairraz,art-culture-and-discovery,48-11114-sitraPCU369956,en.html
A trip on the little train around the town - www.chamonix.com/petit-train-touristique-de-chamonix,art-culture-and-discovery,48-11114-74AASOR800711,en.html
The small park with rides, slides etc., some would be OK for your DD - www.chamonixparc.com/index.php/fr/ete/les-attractions.html
A bit out of town - the mont blanc tram - www.chamonix.com/tramway-du-mont-blanc,86,en.html
If the weather isn't great the cinema often shows English language films if there is anything suitable.
There are also some nice walks in the valley starting from the town centre - my DS loves watching the paragliders coming in to land in the landing spot about 15 minutes walk from town.
If you have a car
The animal park is really nice - but a bit of a walk from the car park - www.chamonix.com/parc-animalier-de-merlet,leisure-and-outdoor-games,48-3111-74AASOR100137,en.html
The steam train park in Switzerland (my DS loves this place!), not too far to drive in a day - www.swissvapeur.ch/
A trip on 3 mountain funiculars/trains to the Emosson Dam is good fun - www.chatelard.net/en/home.xtm
My DS at that age used to love a short walk in the mountains, up on a cable car/railway and a walk back down looking at all the cows etc there are some paths around that are suitable really young children (as you can probably tell there was a great deal of interest in trains as well). I am sure that you could find enough to do for a week there.