Train ticket between Shanghai and Nanjing

We will be arriving in Shanghai at Pudong Airport at about 7.30 am. on Saturday 17th September. We will need to clear customs and travel to Shanghai railway station to catch a train to Nanjing.
Will we be able to buy a ticket for a fast train to Nanjing and travel on that same day?
Is there anyway we can book a train ticket before we arrive in Shanghai?
Is there a train ticket office at Pudong Airport?
Thank you for your help
Maggie