I'll bite (quite literally - not just tongue in cheek). If we're down to 10 species, then the world's going to hell in a handbasket, and I'll need something to eat. So....
1) Ostrich: there's a lot of meat on them
2) Emu: ditto
3) Wood duck (Chenonetta jubata): breeds like crazy, very tasty
4) Peregrine Falcon: not for eating, but to hunt for...
5) Rock Dove: if they can't survive, what hope have we?
6) Quail (take your pick of species - preferably a plump one)
7) Great Cormorant: for use in fishing, as is (was?) done in parts of Asia
8) Junglefowl (or, for preference, their domestic descendants)
9) Short-tailed Shearwater: do a search for "muttonbird pie" on google + a Victorian breeding population of 22 million pairs
10) Little Penguin: do they really taste as bad as they smell?
Food for thought!