No, it's easier than that. Just buy an analog->digital converter. Use the video adapter on the mini and plug that into converter, then plug the converter into the laptop, then use something to watch the DV stream (like iChat). For just a few hundred dollars, you'd have a system that was at least 10% as good as a flat-screen LCD costing... a few hundred dollars.
Seriously: buy a monitor, or be content with pretty slow VNC speeds, esp. as you'd likely be wanting to get them connected wirelessly.