what material for a dust filter?

Wouldn't worry about it, just blow the laptop out with compressed air every now and then, it'll be fine. Was in the computer industry for 10 years, still kinda am even thought it's security based.

cheap as- go grab some gauze from the local chemist.
peel off a sheet or 2 and bung it over the vents. Make sure you can still blow through it easily though. Dont bother cleaning it when its dirty- just ditch the old and grab a new one from your 1st aid kit.
Also worth consideration is that the box without its own fan will likely act as an oven. The fan for the lappy will circulate air inside the the PC, but you may still need one for the actual box. Fans in PCs are 12V so if you know of a dead PC laying around it will save you some cash.

Trev, The map worked out fine.
If you wanted to put a filter overr the hole to keep the dust out, you would need a very fine filter that won't let a lot of air through. Perhaps you could adapt a paper face mask or a coffee filter.
Cheers
Alpaca

Go to a vacuum cleaner place and you can get a electrostatic filter that is made from a gauze type of stuff. Probably the best bet if you want to collect the dust. You might even find something you could adapt in the vacuum cleaner bag section of Kmart/Big W

I dunno if that is a good idea at all. Holding my hand near the fan outlet of my laptop, it is HOT air that comes out of there. Putting your lappy inside a box you have to carefully make sure the air intake slots ( most likely on the back and underneath) of it can get the fresh cool air from outside the box unrestricted.
And you need a good exhaust fan, right opposite the lappy's air outlet, to suck out the hot air before it gets a chance to circulate inside the box.

Now, I do not have an external monitor and so do not know how they are controlled but I would think that a laptop goes to sleep when its lid is shut. Do you think it still drives your display while asleep? And, having the laptop open would defeat the whole box idea, not?

Why not using a desktop computer stashed under somewhere, it would not be any bigger than your laptop placed inside a suitable box. The desktops have bigger fans too and could easier accomodate a filter screen for it. Use your small monitor instead of the original one.
Power for the desktop? You need power for your laptop too, so its just different and perhaps even simpler with only one conversion.

Klaus