All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
First of all, we ask Allaah to reward you for being keen on observing the rulings of Islam and preserving your daughter from falsehood. May Allaah make her a comfort for your eyes in this worldly life and in the Hereafter.
Giving gifts is desirable at all times, but it is forbidden to give a gift for this occasion (Christmas) as it is among the festivals of falsehood. So, if the gift you gave her was not for this purpose, then there is no harm in it.
Thus, if you gave her that gift for a good objective like in order to distract her from celebrating that festival, then you will have a great reward, Allaah willing.
Allaah Knows best.