If the reality is as you mentioned that your daughter did not use actual words in making oath or vow, but she
had the intention to make an oath in her heart only, she is not obliged to fulfill the oath. It should be noted that an oath is not effective unless the person uses the words of making an oath by swearing by one of the Names or Attributes of Allah (Exalted be He), or the like. It was authentically reported on the authority of
Abu Hurayrah (may Allah be pleased with him) that the Prophet (peace be upon him) said:
"Allah has forgiven my Ummah (nation based on one creed) for the thoughts that cross their minds, so long as they do not act upon them or speak of them."
In another narration, he (peace be upon him) said:
...For (Part No. 23; Page No. 47) what crosses their minds.
Muslim in the two Sahih (authentic) Books of Hadith,
ibn Majah, and others)
Accordingly, your daughter is not obliged to observe Sawm, as she has done nothing that requires the fulfillment of an oath or a vow.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.