It might not be so easy. Taiwan's power works like the US, as far as I can tell: you have phase 1 and phase 2 which are at 110V relative to ground. So the normal house supply would be either of those phases and ground. Between the two (180' out-of-phase) is 220V. You may or may not have both phases delivered to your house from the transformer (the dustbin-like thing that hangs from the nearest lamppost). It probably depends how big your building is. If it's an apartment, 99% certain a 水電 guy will be able to find both wires and install a 220V socket, as UhdL said, for not a lot of money. If it's a standalone house, especially an old one, you might not have a two-phase supply actually reaching the building.
If you find yourself in the latter situation, I don't see why you can't get a 110V inverter-fed aircon. It will be rather low-power (<1.6kW), but that should still offer you an effective cooling capacity in the 6kW range. It's easy (from the designer's point of view) to put a voltage doubler at the front end of an inverter, so there must be dual-voltage 110/220V aircon units out there.
EDIT: just wondering ... when you say 'inverter', do you mean heat-pump function (an inverter is just an electronic circuit that converts DC to AC, in this case for motor-control purposes)?