Quite honestly, I don't see this mare doing well in halter classes. *Maybe* at 4H level, but that's a steep maybe.
I'll start from the top down...
She's got a bit of a hammerhead and her throatlatch is coarse. I don't like the way her neck ties in; it looks like it's set on rather high, especially for a quarter horse. She looks a wee bit pigeon breasted. Her back is a bit long and she's butt high. She's got a rather steep croup, especially for a QH. I do like the depth of her heart girth, though.
She's a wee bit over at the knee and tied in behind the knee. I do like the slope and length of her pasterns though. Her hocks are set nice and low and I like the angles of her hind legs, however her gaskin looks kinda long to me.
She isn't a halter horse, I agree maybe try showmanship?
In all honesty at the end of the day is comes down to the judge and what he/she is looking for but for me personally, she is not a halter type :)
As everyone else has suggested, I would go ahead and show her in Showmanship. Even thougth your daughters mare has some conformational faults, I would go ahead and train her and show her is Halter.
She's going to need to know how to set-up and to do it quickly. Also be able to get her ears forward when asked (Judge is doing a final look before walking away).
My mare does not do well in halter, unless it is a man judging or a woman judge who does eventing, then they like my horse. She's an Appendix and is very thoroughbreddy, also has been described as very feminine(?). She is not the stock type. I asked a quarterhorse judge (who she herself won numerous world titles) and was putting on a clinic. I asked her about not showing her in halter and just doing the Showmanship. And she told me to do the halter classes because it preps them mentally - think of it as a warm-up to showmanship and not to worry about how I place.