Train on the 3rd of October 2014

Hello!

I am supposed to take the train from Hong Kong to Beijing on the 3rd of October but heard it was National Holiday in China.
I haven't booked a train ticket yet thinking I would/could buy it once in HK.
What are the chances of having the trains completely booked on the 2nd/3rd? Is it possible to purchase a ticket online, if yes, what would be the best site to do it?
I have tried to look at MTR intercity but it doesn't offer Beijing West as a destination.

Many thanks :)

Samy