If you are using an iPhone there are libraries available that you can implement to give the effect of mirroring to allow you to use an adapter and projector.
The following library is what I plan on using, though have not implemented quite yet(If its possible, I will do so by the end of the week as this is what was recommended to me). Of course you will need to include the rest of the files, the one I have linked is merely the .m.
http://code.google.com/p/iphoneos-screen-mirroring/source/browse/trunk/UIApplication%2BScreenMirroring.m
It is worth noting that this is NOT supported by Apple as I believe it uses private Apple API's and as a result will not be approved for the app store. I would recommended branching of a version of your current project and implementing this to demo, so you still have a clean version of your app.
Edit for clarity: Only the iPad 2 supports native mirroring for what I believe is all apps through an adapter, the iPad 1, and all iPhones dont support mirroring by default through adapters for anything other than apps developed by Apple.