Will it be kept in a garage or outdoor? If indoor, hook the battery up to a charger (I have a Noco G3500, but any smart charger will do). If outdoors, you can get one of those solar chargers and leave it attached to the battery. I use this for my cars that sit outside and it works very well.
Your inverter will not be damaged. Some people go on longer than 4-5 months without driving and their vehicle starts up fine so long as the 12v has enough charge.
EDIT: Also, disconnect the negative terminal on the 12v battery to prevent the car from drawing power.
Last edited by GSteg; 11-30-15 at 03:51 PM.