1000W (plus efficiency losses) is a hell of a lump to take from a battery (100amps+).
A mug of water may only need 3 mins to boil, but a ready meal or a fresh fish can take 10 minutes or so, which would be a tenth of the capacity of a 120AHr battery.
You may also find that you need the more expensive 'perfect sine wave' type of inverter in order to run the microwave. They do make 12v microwaves for caravans and boats, but very expensive imo.
this for example:
12v microwave
Best plan on a seperate battery on a split charge system. Mains electric kettle is usually considered a no-no for the same reason, current drain is horrible, but again, 12v versions are available, usually low powered, and not too expensive
john