You stiill remember this girl from six months ago? You may not see her again so this may be your only chance to make that move.
Approach her either before or after the hair cut - just make sure you are naturally available during these times - in other words don't look awkward by running up to her as she is leaving.
I would approach her at the end of her haircut - if my mom was working there , Id ask her to let me stalk, I mean stay in the back room until she finishes her haircut and then when your mom is away for a second (have her do this) compliment her on her new look and how well it fits her face and how that her new look would be well complemented (not to confuse with the word complimented) with a nice dinner outfit and you would be willing to accommodate her with this task this weekend at so-and-so restaurant - and would she like this idea -- say this in jest and sometimes smiling but seriously when you make the offer.
Use your mom as an accomplice, if it is not too demeaning - an introduction beforehand may ease the tension later or it just may show your intentions and give away your plans - you decide.
If an opportunity presents itself before the haircut then by all means don't wait after the haircut!
Don't pee in your pants over-thinking the approach, so make sure you use the restroom before you arrive.
