Is it possible to do a train trip from Basel to Kanderstag in one day?
Sure, it's only 2 hours away by train with a change in Bern. There are 1 or 2 departures an hour.
Anything is possible with the swiss train system. Just check the times to see which are faster/more-direct for commuters. The swiss "president" takes the Bern-to-Zuerich train daily office to home so commuters have plenty of options - so join them to save time.