Slow cooking

Hi folks, We just bought a slow cooker/risotto maker for use at home. We're now wondering if it is possible to use it in our '13 FC28, while we're driving. It is 120v only, so we'd have to plug it into an "inverter" outlet. Can we do that safely? Most slow cooked meals take several hours - can the inverter run that long? Is there a risk of over-heating the inverter?

Can this be done while we're traveling between campgrounds, for example? We picture putting the cooker in the sink so it wouldn't fall or tip.

Thanks, Dave