See the sun moon lake from Taipei

Yes, but I think it is a little bit rushed to visit the Sun Moon Lake from Taipei in one day.

You can take the high speed train from Taipei for about 1 hour to Taichung and then take the shuttle bus from Taichung railway station to the Sun Moon Lake. The bus ride needs another 1 hour. So you are suggested to start very early in the morning if you intend to visit Sun Moon Lake in one day from Taipei.