The Korg MicroKey 25 is a very tiny, but very feature-rich, MIDI keyboard that you can connect to an iPad. It supports any of the core MIDI apps, and connects to the iPad through the Camera Kit (which provides a USB port). It’s velocity-sensitive, so it can tell the difference between a gentle touch and a heavy one. It also gives you an octave shift feature, and lights on the keyboard tell you what octave you’re in.
It allows you to have a very capable keyboard wherever you go. It retails for $110, but right now you can get it at Amazon for just $70.