Newly-promoted Posh will visit Pride Park on August 8 ahead of back-to-back away games for the Rams at Scunthorpe (August 15) and Blackpool (August 18).
Clough's side conclude August with a trip to the City Ground to face East Midlands rivals Nottingham Forest, with the return fixture at Pride Park on January 30.
The festive period comprises home games against Doncaster and Blackpool before finishing 2009 with a tantalising trip to St James' Park to face Newcastle on December 28.
February will be a difficult month for Derby with Newcastle, Preston and Swansea the visitors to Pride Park, along with away games at Sheffield United, Reading and West Brom.
The Rams will finish the campaign with a home game against Cardiff on May 2.