Train tickets from Beijing to Pingyao at the beginning of October

Hi,

I will be arriving at Beijing on October 1st and wanted to stay some days, probably until 4th or 5th October before going to Pingyao via Taiyuan and afterwards to Xi'an.

Now i am a little bit worried that it might get complicated to get train tickets. Should i book them in advance at this site? Is it possible to book the tickets in advance on this site?

Thanks in advance for your answer