How to use the camera of an iPad connected to a Mac as a video camera?
I'm not aware of any software the directly captures the video from the camera, but like others have suggested you can capture the screen, which also works when the camera app is open, thus getting the camera video. After doing some research, it seems that you can record the screen right through Screenflow. Check out more about Screenflow screen recording here.

The next option, which is free, is to use the built in QuickTime application to record the screen of the iPhone. This can be done by


Open QuickTime
File -> New Movie Recording
Next to the record button, click the down arrow to the right
Select iPad Mini
Open the camera app and press record in QuickTime


The downside to these two options are that you won't get the native resolution from the camera, instead it is being downscaled to fit the screen size. For both Screenflow and QuickTime, you must plug in your phone, but this will provide better quality screen recording than doing it over WiFi. Best of luck!