1300W will be the amount of power (or VA) used on cycle (one expects during heating the water). Your heating element in expresso machine draws a lot of power because it has to create heat under pressure.
1300W is going to require a fairly substancial inverter - though you should
be able to get away with a modified sine wave inverter.
For the amount of time you would have it on, say 15 mins to allow preheat and to make a cuppa or two, using a modified sine wave inverter with an efficiency up aroun 80% you would draw close to 30Ah from a battery.
IMO get one like displayed in the link above and put it on your gas stove, we have one that does 2 cups at one - brilliant!
The other thing is those all in one machines are nice (we have a gaggia at work) - but the true beauty in good coffee is a coffee machine with out a pump but a manual handle - much better coffee as you get control over the flow rate thus a better creme
so something like a LaPavoni might be better for your wife. Do an E-Bay search for stove top expresso machines.
Oh and Dark Maragogype is a very very nice bean. Dark Mocha is also good if she is a caffine addict.
You can get inverters upto 1500W from 12V in modified sine better option is to run a 24V system - your current draw for the same amount of power wont be as high. stove top coffee machinestove top coffee maker 2
Oh and http://www.thebeanery.com.au