That is accepted.

When a possessive pronoun is not present it is assumed that the object/person belongs to the subject. In this case thus MY daughter.

English is obsessed with possessive pronouns. It makes sense because their presence allows you to omit an article. Czech, not so. If the daughter was somebody else's you would say so. Jane's daughter, etc. Or rather "Janina dcera".

Sentences like "he puts his hand on his heart" when translated word by word sound silly in Czech. We would be confused as to who else's hand but his would he be putting on who else's heart?