we went to Just Cuts for DD1 only a couple of months ago, she has quite long thick her for her age but is happy to leave it in a ponytail.
It is normally $15 and when i had asked about her first haircut that is what they told me until i specifically mentioned i thought their first was free under 2yrs old.

They asked if i wanted a fringe cut but i said no as her hair grows so quickly it will just be in her eyes in a week anyway...

They were AWESOME with her, they bought out a little portable DVD player to keep her occupied, talked to her and told her what they were doing, she didn't move, didn't cry or anything i was so so proud of her.. i even got a photo on my phone

GL with it all, i'm sure she will be fine.