Hi. I'm Dr. Lee and will do my best to help.
No. Dogs do not normally require tetanus shot from cuts. Depending on the depth and severity of the cut, stitches might be needed. The only constant is the need for antibiotic, usually something called Clavamox is best. If she hasn't been to your vet to have the wound checked out, you should do that soon.
Please let me know if you have any questions or concerns. Thanks.