Tinstart, amps are different when speaking of 120V or 12V system.
Dometic draws 3 amps @120V = 30 amps @12V. This is 360W.
Expect about 150-200W from small residential fridge. Much better than 360W of Dometic in electrical mode, but still too high to run it on a battery. Without hookups or big solar you are facing long hours on generator.
It jumps to 1500-2000W during start-up, so your inverter (or generator) should have at least 1500W.
(I see that the one by Dutch is not too "jumpy" on start-up, but still 1000W with inverter losses).
On 30A hookup this won't be a problem, but it "might" trip the breaker if you are running roof top air on full power at the same time.