I just went through this, so I think I can help.
To begin, you need to set up screen sharing on the mini. It can be done with an HDMI to a tv if you have one. But you will still need a keyboard and a mouse. Once it's set up, you have to have the mini open iTunes, or whatever music server program you are using, upon startup. This is done
in the users section. After that you need a screen sharing app for your iPad. I have tried two - Desktop, and itap. They both have some glitches, but you can get done what you need to. Once it's up and running, I use the Apple remote app to play music. That works really well.
Hope this helps.