In the county I live in (Ohio) we can actually get Temporay Event licenses. Still has to go through the Health Board for approval and they are a little more thourough in the inspection, but if you aren't planning to vend full time and just want to do something like a car show or 2 per year, it's a perfect option.
I've seen some other types of these setups and they have the 10x10 canopy or gazebo style tents with 2x5' tables for the service and tables along the sides for prep with the cooking and Sinks in the back. Been considering a trial run of something similar myself to plug some BBQ in the mix, but still working to get the sinks, fresh water, etc to be a mobile setup to accomplish it.
Good Luck...Hope it works out great for you.