Welcome to the Forum.
That is a great time of year to visit Switzerland. We have come over in September most years of the past 15 or 20. I wish I were coming over then in 2015, but this year we're going to the UK, for a change.
Arno and Annika (the moderators) are really good with itineraries, and I'm not.. But, I have one suggestion.
Instead of Interlaken stay at Wenggen or Grindelwald ( or, maybe Mürren.)
All have much nicer scenery and more interesting walks than Interlaken.
I prefer Wengen. See this link, good for the region as well as Wengen.
Mürren (and close by Gimmelwald) are very popular, but require extra time and travel to get out of the valley if you decide to travel beyond Interlaken (Brienz. lake boats, Thun, Bern) if you are unlucky enough to have clouds in the mountains.
You can get some ideas here:
Train (and other transport ) schedules here:
and a topo good map here:
map.geo.admin.ch/?X=166260.64&Y=641194.6 6&zoom=3&lang=en&topic =swisstopo&bgLayer=ch. swisstopo.pixelkarte-farbe
If you zoom to the close up views, mousing over a location with a train(bus, etc.) station gives you transport schedules. First you have to click on the box by Traffic (on the leftmenu) to make the symbols appear for the stations (only at high enough magnification of the map.)