You are not giving your daughter a gift. You are loaning money to her with the expectation that all of it is being paid back to you. She will not be giving you a gift when she re-pays the loan. So, no, there will not be a Form 709 gift tax form involved.
However, you need to be aware of imputed interest when you loan money to a family member.
https://turbotax.intuit.com/tax-tips/tax-payments/irs-tax-rules-for-imputed-interest/L7UbulHpC
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