Arno has referred you to the Grabünden, including the Engadine (Inn Valley).
Most of his suggestions are in the Upper Engadine, including St. Moritz, Pontrsina, some famous train rides, and also nearby valleys - the Albula , etc. This is certainly the best known part of the region, for good reason. There are many attractions, including those suitable for your child. A horse drawn wagon-ride up the Val Rosegg could be one. The cograil ride up to Muottas Muragl, and the generally easy walk from Muottas Muragl to Alp Languard with ski lift down to Pontresina, could be another.
The Lower Engadin, also part of the Graubünden, has fewer tourists, and is less well known.
After several years of staying in or near St. Moritz, and exploring the Upper Engadine and the surrounding area, including St. Moritz, Tiefencastel, Preda, Bergun, Pontresina, Champfer, Val Rosegg, Brgaglia/Bergell.....we now tend to go instead to the Lower Engadine, at the other end of the Valley, near Austria.
Fewer tourists, more access to nature ( including the "forever wild" Swiss National Park) -
wanderland.ch/ en/hiking-in.html? phrase=Zernez& sname=&sid=
That region may have hikes that are difficult for a 6 year old, so look at the maps carefully.
One that might be good for a 6 year old is to walk along the ridge top from the lift station above Ftan to Motta Naluns, or the reverse. Great views.
Access at one end is a lift near the Scuol Bahnhof, up to Motta Naluns. Walk moderately down hill to above Ftan ( at Prui or Nateas) and take the lift down to Ftan, then catch the bus back to Scuol Bahnhof.
There is a usually herd of free-range goats at Motta Naluns which will likely please the 6 year old, as well as the rest of you.
There are beautiful old towns, such as Guarda, Ardez, and Scuol.
nytimes.com/2010/ 05/09/travel/ 09next.html?_r=0
Some pictures are attached
This region is not usually included in a first trip to Switzerland, but you have a generous amount of time and might consider it in combination with the more famous Upper Engadine (St. Moritz.)
A comment on nomenclature.
The Engadine strictly speaking and narrowly defined is the valley of the river Inn ( En, in older dialect.) The term often includes the region.
"Graubünden" refers to the entire canton, and means "Grey League", a name that dates back to the early history of the region. It includes Chur. It is the region in which the fourth Swiss national language (Romansch) in all of its local variants is still preserved from the middle ages and spoken.
en.wikipedia.org/ wiki/ Graub%C3%BCnden