I think you should probably incorporate. You face all kinds of liability -- your van could cause an accident, a dog could jump off the grooming table & hang itself, some child could grab your scissors & be hurt, etc. If you incorporate, the corporation can buy a general liability insurance policy & pay the insurance on the van. This would protect your assets if something disasterous happens & you don't have anough insurance to cover it.
You can get self-help legal books on incorporating at the library. Pick one that covers all 50 states & includes forms. it will probably include state business license info. Then decide if you want to do it yourself or hire an attorney to do it for you.
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.
