Yep - you've got the correct.
Start with the DOH. They'll give you the framework for what you'll have to have to be legal - that usually entails a commercial kitchen that will be certified by the DOH & regulations on your serving set up. (For example - I have a commercial kitchen but no trailer. When I do a mobile gig - DOH specifies what kind of tent, water supply, holding temp, etc. I need at the mobile location.)
Once you have the DOH regs, you'll need to check with local building & fire codes to build out your kitchen. Once the kitchen is in place - you'll need to talk to your insurance agent about covering the kitchen, mobile set up, liability, etc.
Cha Cha Hut BBQ : 43311 Route 28 (corner of Route 28 & County Road 38: Arkville, NY : [URL="http://chachahut.com"]chachahut.com[/URL]
Backwoods Pro Jr.
busted Backwoods Fatboy
Weber 22.5 Kettle
some stainless wood fired thing