I haven't jungled Annie this season, but I know it was possible in Season 2. Assuming you get common AP jungle Runes and Masteries, running through the Jungle in 4 or less minutes should be feasible, even if you are at half or so health. As said above, a strong leash would probably be necessary.
Goal would be to jungle til about level 3 or 4 and probably gank mid first with a stun ready. After that, tele back to base and jungle and gank normally like any other jungler. Annie has good base stats early levels to deal damage plus her stun makes ganks great. However her lack of sustain is a bit of a problem, which I think 9% Spellvamp may help out with.
I believe you start off with E the new Hunter's Machette item and 5 health pots.
Masteries: 9/12/9, or 21/9/0 or 0/9/21 (Defence masteries are a necessity)
Reds: Attack Damage, Attack Speed or Magic Penetration.
Blues: AP per level, (your choice honestly)
Quints: Movementspeed, Spellvamp, (your choice honestly)
You can decide to build either an early Liandry's torment or Spirit of the Spectral Wraith.
Core items would be Boots of Mobility, Liandry's Torment, Spirit of the Spectral Wraith.
finishing three items would be your choice.
As soon as I get back on LoL this weekend I plan to try this out to make sure my predictions aren't baseless.