I need to book a taxi from Beijing airport to my hotel at 11pm 13th April - can I do this on line?

As I know, the taxi booking online is only available for Chinese people, because the website is in Chinese without English version.
For your situation, you can ask the hotel you live to help you to book a taxi in advance, or book a pick-up service from an agency, or take a taxi directly from the airport to your hotel. The taxi is very easy to take in the airport, you may choose the last method.
By the way, the booking taxi can be done by phone and the number is 96103. Hope this number can help you.