Looks like a very manageable trip. Personally I would opt for a cycling vacation in the mountains instead, but given the season it is too early for such a trip. I don't think you should have any trouble with the first two legs on any bike. The return looks a bit long unless you've trained for that distance... especially if you're not on a road bike.

In my experience the national routes are in general great, but unfortunately they tend to have a lot of unpaved parts so if you are on a road bike you will need to prepare the routes carefully to avoid those portions (they are dotted lines on the national bike route maps). Also it can be very difficult to follow the signs. Be prepared to lose the path a number of times, backtrack, and figure out where you are (if you don't see any more bike path signs at intersections, you have probably gone off track). Also use www.mapmyride.com or google earth to plan out your route and see how much elevation change there is... a lot of climbing up and down without training for it can quickly lead to bonking and make it a very unpleasant trip.

edit: you should be able to find a route that doesn't include mountains / extreme climbing. If you follow a route near the train tracks it should be relatively flat. There is not too much terrain to worry about between zurich and interlaken... should be obvious when looking at google earth how to get there without going over the hills (and the snow is up in the hills, generally not in the valleys).