Is it possible to use a Mac mini as a docking station for a MacBook Pro?
The concept is nice.  But you can't connect a Mac mini to the MacBook Pro and have the mini act like a docking station.
Nevertheless you can enable file sharing on the Mac mini and all directly connected storage devices (USB, Firewire, SD) become available to the MacBook Pro via SMB networking.
Other devices can't be accessed as if the Mac mini were a docking station.  That would include the audio port, non-storage USB/Firewire devices and HDMI.  I don't know of any software solutions which enable this.
Other things you might consider:
Screensharing allows you to show the desktop (and use the mouse and keyboard) from one computer to the other.  And there are better performing products (e.g. Jump Desktop) than the inbuilt screen sharing.
You can find software that will enable the mini's screen to act as an extension to the MacBook Pro's screen.  My limited experience with this has not been very successful.