Is it just a case of removing mouse and keyboard from old mac after booting it into TDM and connecting them to Mac mini?
You got it in one. In fact, I am not sure you even need to have the monitor connected to boot into Firewire target disk mode, but I haven't tried it so I don't know for sure. I do know lots of places run MacMinis headless with neither a monitor or keyboard configuring them remotely through VNC connections.