It's a 120/12v fridge. Do not run off of an inverter. There is no need to and as mentioned in another post converting power from 12v to 120ac really taxes a battery.
How many amp hour is the battery? My guess is you get 1-2 days but if you run the battery down to low you will kill it.
Put a good battery in your vehicle and keep it topped up with a solar panel. 100 watts preferred.
Read this article:
http://www.arkportablepower.com/blogs/news/17808136-the-arb-fridge-freezer-and-battery-life-what-you-need-to-know
Also get on ExpedtionPortal.com and read threads in the power section. This topic gets discussed every week.
Feel free to critique my setup. I have had many iterations and have come to like this one.
I have the following:
X2/Northstar Group 27 91AH battery
ARB Wiring Harness (i.e. at least 10 gauge wire)
Renogy 100 watt solar suitcase
Jump box in case I kill my battery (pretty unlikely)
The Renogy suitcase is big and bulky but gives you the most bang for your buck. I also have a Powerfilm rollable 60 watt panel as well. At $500+ those are out of most peoples price range. The Renogy is a great setup. You just have to protect the charge controller because it is not waterproof.
For long base camp trips I can also bring my ArkPak battery box which has a smaller 55ah battery. The solar panel just gets moved to that to keep it charged up.
You can talk about Dual batteries, big batteries, batteries in series, I don't really care. At some point your batteries need to be charged up. Get a good solar setup and skip wasting gas while running your truck for over an hour to charge your battery back up.
Also, traditional batteries are not like what is in your phone, tablet, whatever. They don't run from 100% to 0%. A traditional deep cycle battery is at 50% charge or less at 12.3 volts. Keep taking a battery below that and as mentioned above you will kill it.
Will your setup work? Of course it will. Plenty of people do that but it isn't the best route to go. There are too many factors involved to give you accurate information.
How large of a battery?
How old is it?
What temperature do you want to maintain the fridge at?
How full is the fridge? The more full the more efficient they run
Did you pre-cool the fridge and food on AC power before your trip? 2 days is best
How hot is it in the vehicle where the fridge will be stored?
