Travel time would be quite long (and that would be what would knock it out of the running in my book), but I think it would be fabulous!
Anywhere in Latin America would be great...Brazil, Costa Rica, Mexico, etc.

Other December vacation possibilities (that are closer to Doha):

Egypt - Sharm Al Sheikh/Red Sea would be nice
Maldives - but it's pricey!
Thailand - can't go wrong with Thailand!
Indonesia - Bali and Lombok are lovely -- still some unrest in the country, though, and it may rain a bit
South Africa -- can get quite hot, but great animal parks
India - Goa, Kerala, other more southern areas will be warm
Mauritius and Seychelles - warm and tropical but possibly rainy

The world is your oyster! Have a great trip, wherever you go!

"Marriage is a wonderful institution...but who wants to live in an institution?" -- Groucho Marx