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First of all, it does not matter if she prepaid gift tax or not, the person that receives the gift does not pay gift taxes on the gift, see link: https://www.irs.gov/businesses/small-businesses-self-employed/frequently-asked-questions-on-gift-taxes
The only way for your daughter has to pay this tax is if she has a written agreement to do so. If not, the gift tax is always paid by the person giving the gift. In 2015 there is a $5.45 million dollar lifetime exclusion for gifts where no tax is paid (again this is for the person giving the gift) so there should be no worries for your daughter to receive a gift such as this.
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