Is it possible to get the native iPod Touch and iPhone apps on the iPad?
Since these apps are packaged as part of the Core iOS image, you will need to jailbreak the iPad OS to allow modification/installation of the apps currently shipped as part of the iPhone / iPod touch such as Calculator, Clock, etc...

The best technical description of /Applications on iOS is from The iPhone Wiki where it calls out the differentiation between iOS images and major release versions. I haven't ever used it, but the jailbreak package "Belfry" purports to do precisely what you ask and might make interesting reading as well in case you change your mind about jailbreaking in the future.