The cut will not maintain the frizziness - that is down to care/products. I'd say google the curly girl method but you would probably drown in results, conflicting advice and give up (not a reflection on you at all - just on how much is written about it).
But in essence to get rid of the frizz she needs to:
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Throw away her hairbrushes. Never, ever brush curly hair. Only detangle with a wide tooth comb when wet/covered in conditioner. It is very fragile and yanking at tangles in curly hair = breakage = more frizz.
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Moisture. In the form of lots of conditioner. Curly hair is drier - the natural oils do not travel down curly hair like straight hair. She is unlilkely to ever, ever have greasy hair. But you need to condition it. By a) not stripping the natural oils with harsh sulphate shampoos. And lots, and lot of conditioner. In fact a lot of curlies wash their hair with conditioner. I do. A silicon free conditioner (which means it is water soluble so does not need stripping from the hair with soap-y/foam shampoos_. The scrubbing motion is enough to wash the hair and scalp. Especially as it is not prone to oil. So "wash" with conditioner. Then condition. Comb though with a wide tooth comb and then really really squish it in. Gently cup the curls from the bottom towards the scalp. Squish, squish, sqush. Rinse. Then if particularly dry hair take a 10p blob of the same conditioner and comb through and leave it in.
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Blot /squish dry with an old tea towel or microfibre towel. Then rake through some curly friendly gel (see below) a big blob of it. Squish that in again. Gently, towards the scalp. Do not scrub with a regular towel as that = frizz.
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Leave to dry. It will dry crispy as the gel "sets". This is good. You can gently diffuse. Do not brush. When dry do the gentle squish movement again which will break the gel cast and leave her with soft curls with no crunch. She may not need the gel. Maybe try to start with with out. But the gel helps define to curl and stop frizz.
5)To sleep - put her hair in a pineapple- high pony tail on top of her head. This will help protect the curls.
Invest in a satin or silk pillow slip. Again, helps protect the curls.
In the morning take out the pony tail and leave it to settle for a few minutes. Then some neat conditioner again about 10p size rubbed in hands and applied neat over the top layer of hair should ease any frizz. Or try a spray bottle of water/conditioner mixed. Depends on her hair how much extra moisture she needs in the mornings.
It is a trial and error method. What products you find works for you may not work for someone else.
But
Moisture (condition)
Protect (nothing harsh and don't brush)
I personally use Faith in Nature Dragon Fruit conditioner to wash, their Rose conditioner to condition/leave in . I then use Umberto Gianni Curl Jelly as my gel. Refresh in the mornings with slightly watery Rose conditoner.
But they may not suit your daughter's hair. Hers could be thicker, finer, curlier, wavier.
However - conditioners - avoid silicons. Avoid sulphates. Gels avoid alcohols (I think). Some hair loves conditioners with coconut - some hair hates it.
Sometimes it is the cheaper products that are "Curly-Girl-Friendly" - so Tescos tubs of cheap blue gel used to be. Alberto Balsam conditioners (poundland) - some of these are. What I would suggest is using www.curlsbot.com Cut and paste online ingredients list into it and it tells you if gentle enough to use. And try cheaper products first.
Lorraine Massey did a book, Maybe buy a copy for your DD (rather than going down the rabbit-hole that can be on line). She will have curly hair for life.
Once you have tamed the frizz a bit then yes a haircut. But the cut will not tame the frizz.