No subpanel. Internal transfer switch is probably not 30a rated so whole house you need to buy a separate transfer switch.
I recommend:
1) Remove that cover and insert a new 15a breaker. Connect the converter direct to this new breaker.
2) The existing 15a breaker that goes to all outlets will feed the inverter input. Remove the romex from this breaker (hot, neutral, ground) and connect the romex to the output of the inverter. New piece of romex connects all three (H,N,G) from the panel to the inverter input. Connect your 12v and you are good to go. (Put the fridge on propane)
