Not to poop on the parade, but...
Typical auto alternator produces 65A.
You need about 5A just to keep the car running. Down to 60, or 720W.
Your micro is 600W (could be much more, 900 is typical these days).
It wastes 300W due to inefficiency. Others already covered this turf.
Your inverter also wastes power. Figure 50% of what you are using gets converted to heat (but not where you want it)

.
So 900W + 450W, you need 1350W.
Where does all that power come from? If the alternator can't deliver, you get it from the battery.
Alternator delivers 720W, battery delivers 630W, everybody's happy.
Now a good battery in peak condition will crank a car about 5 minutes. It is delivering maybe 40A to do that. OK, 630W is 52.5A, or a bit more than cranking a car. So maybe figure 4 minutes of microwaving before you won't be able to start the car again.
All this is just guesstimating, and YMMV. And you could run the car for half an hour after nuking that popcorn to put a bit of charge back in the battery. And you could get a heavy duty alternator (delivers about 95A) for several hundred bucks and sneak up on that power deficit a bit. Or you could spend $200 on ebay and get one of those cheapo 2 cycle gennys, and not spend it on an inverter.
I'd really urge you to consider a generator. Cost wise it will be a wash, and the genny will never leave you stranded, but it does add weight.
In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away.
-- Antoine de Saint-Exupery