You might not fall under the local health dept's pervue if you are cooking in someone's home or other "on site" places. For example: in my area I can have six coffe pots running 24/7 in a commercial retail establishment and bring in pastry from outside and unless I have coffee syrups with pumps to dispence the syrup the health dept has no jurisdiction. Sugar, creamer etc doesn't count either, just the pumps because they have to be rinsed. Crazy, but true.
Your best bet is to call city hall because it sounds like the only license you might be under pressure to get is a business license for tax collecting purposes. Call the health dept first to see if they regulate your type of service at all (in most Southern states there is no sales tax on a service so you don't have to charge it or collect it). Then check with city hall for the same type of business license that a cleaning service might need.
If you keep refering to your business as a service you might save yourself some tax related headaches. Might not be true for your area, it just depends on local business regulations.