Glen

You need to do your homework a bit better.
There is only 1 flight a week on Saturdays returning the same day using a 737 with only one class of service.

LanPass do offer awards to Mount Pleasant at 60000km.

Its pure conjecture on my part but I think you've got more chance of seeing penguins in the Sahara than getting an award ticket for the dates you are looking at for the following reasons:
1) Lan Chile has blackout periods for award availability -not sure which dates but almost certainly Xmas and New Year would be included.
2)High season to the Falklands is a very brief Dec-Feb for obvious reasons.
3)The flight also stops in Puerto Montt and Punta Arenas in Chile before heading to the Falklands/Malvinas so there are also the domestic Xmas travellers you'd be competing with.

You can definitely do it on a Oneworld explorer ticket though using South American segments - I'm holding a ticket to MPN for 1st week in December although I still haven't decided if the penguins would hold my interest for a week - if you do manage to get an award ticket though let me know and I'll look out for penguins next time I'm in Morocco.