I sat down beside her and she watched me having my haircut and then got her to sit down on my lap for her haircut. At the same time telling her it's not going to hurt and she will look better after the haircut.
Bring the toddler to the hairdresser whenever whoever is having a haircut. Kind of helps allay anxiety. You may want to ask what is your child is afraid of.
Mama of 2 cheerful daughter