Who claims the distribution on a 1099-Q - the account owner or the beneficiary?

If you used it for qualified education expenses, it is not considered taxable income and no one needs to report it.   You can use funds from a 529 account for more than just college and other postsecondary education expenses. There’s no federal income tax on 529 plan withdrawals used for:

• tuition at an elementary, middle, or high school (up to $10,000 per year)
• student loan payments (up to $10,000 per beneficiary)
• apprenticeship program fees, books, supplies, and equipment

See 529 distributions

The person or entity who manages the education program typically reports annual distributions on Form 1099-Q to the IRS and to the beneficiary of the education savings account. However, the account owner (such as a parent) will receive the 1099-Q instead if the distributions from a 529 plan aren’t made directly to the beneficiary or to an educational institution for the benefit of the beneficiary.

When the beneficiary enrolls in school and starts taking distributions to pay school expenses, the account manager will begin sending Form 1099-Q each year. And as long as the distributions are used to pay only qualified education expenses, the recipient doesn’t pay income tax on the distributions.   See 1099-Q

Q. Who claims the distribution on a 1099-Q - the account owner or the beneficiary?

A. It can be either. In your case, it's you because the money was sent to you. You are the "recipient".

You need to coordinate with her on the allocation of her expenses, so that she can claim the tuition credit on her tax return. Room & board are eligible expenses only for the 1099-Q and not the tuition tax credit. 

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Qualified Tuition Plans  (QTP 529 Plans) Distributions

General Discussion

It’s complicated.

For 529 plans, there is an “owner” (usually the parent), and a “beneficiary” (usually the student dependent). The "recipient" of the distribution can be either the owner or the beneficiary depending on who the money was sent to. When the money goes directly from the Qualified Tuition Plan (QTP) to the school, the student is the "recipient". The distribution will be reported on IRS form 1099-Q. 
The 1099-Q gets reported on the recipient's return.** The recipient's name & SS# will be on the 1099-Q.
Even though the 1099-Q is going on the parent's return, the 1098-T should go on the student's return, so she can claim the education credit. 

She can and usually should claim the tuition credit before the parent claims the 529 plan earnings exclusion (unless her income is too high).  The American Opportunity Credit (AOC or AOTC) is 100% of the first $2000 of tuition and 25% of the next $2000 ($2500 maximum credit). The educational expenses you claim for the 1099-Q should be reduced by the amount of educational expenses she claims for the credit. Room and board (R&B) are also qualified expenses for the 529 distribution (even if she lives at home), but not the AOC (R&B are also not qualified expenses for a scholarship to be tax free).
But be aware, you can not double dip. She cannot count the same tuition money, for the tuition credit,  that gets you an exclusion from the taxability of the earnings (interest) on the 529 plan. Since the credit is more generous; use as much of the tuition as is needed for the credit and the rest for the interest exclusion. Another special rule allows her to claim the tuition credit regardless of whose money was used to pay the tuition.
In addition, there is another rule that says the 10% penalty is waived if you were unable to cover the 529 plan withdrawal with educational expenses either because she got scholarships or the expenses were used (by her or the parents) to claim the credit. 

Total qualified expenses (including room & board) less amounts paid by scholarship less amounts used to claim the Tuition credit equals the amount you can use to claim the earnings exclusion on the 1099-Q. 
Example:
  $10,000 in educational expenses (including room & board)

   -$3000 paid by tax free scholarship***

   -$4000 used to claim the American Opportunity credit

 =$3000 Can be used against the 1099-Q (on the recipient’s return)

Box 1 of the 1099-Q is $5000

Box 2 is $2800

3000/5000=60% of the distribution is qualified, so 40% of the earnings are taxable

40% x 2800= $1120

There is  $1120 of taxable income (on the recipient’s return)

**Alternatively; you can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including room & board (even if he lives at home) to cover the distribution. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. Again, you cannot double dip!  When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records, in case of an IRS inquiry.

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 

***Another alternative is have the student report some of his scholarship as taxable income, to free up some expenses for the 1099-Q and/or tuition credit. Most people come out better having the scholarship taxable before the 529 earnings. A student, with no other income, can have up to $15,750 of taxable scholarship (in 2025) and still pay no income tax.