there is a big surge when it starts up...its the current in-rush.
You would need a current meter that has a special mode called in-rush mode; and of course its pricey hehe
you could just try a somewhat safe rule-of-thumb in that the inrush current will be 3x the normal draw (yes, thats 3 * 1350 = 4kw!)
I am sure somebody on these forums has sized an inverter for a large microwave and can give you some real-world numbers.