I want to do the same thing and I think this is the right way.

Mount the extra battery and to charge it, just run it with the stock battery, in parallel. You can get a battery isolator from a travel trailer supply shop, that's what they use in an RV or trailer. That way the power inverter only drains the second battery, not the main one, unless you choose to.

I have a 1000 watt inverter to mount in my Liberty one day, hope this helps