Firstly, you. Since you are claiming her, you enter both forms to determine if you are eligible for any education tax credit. In some cases, part of the 1099-Q earnings are made taxable so you can receive an education credit instead. You can't receive a credit and exclude 529 earnings on the same expenses.
"Double dipping" would only be a concern if the qualified expenses (after scholarship) are under c $5000. If your daughter's education expenses (including room and board) are high enough, you can exclude the earnings as shown on the 1099-Q and perhaps qualify for a tax credit on top of that.
You would only need to go through the motions of entering these forms on her return if some of her 1099-Q is to be taxed.
