Do the iPad 2 and the 6th generation iPod Nano have the same docking connector?
The iPod Nano 6th gen uses a 32 pin connector, the same found on iPod classic, iPhones, and more importantly in your case the iPad/2  you will find all the specficatons for docks on the Apple support website. Although it doesn't mention the 6th gen Nano.

This omission makes things slightly unclear however if you check out the product description for the Apple dock connector to USB cable you will see it is compatible with the 6th Gen iPod nano.