'Beloved' is almost like an intransitive, the person doing the loving is not immediately known. Beloved just means that someone, somewhere loves them. Of course, through context we quickly discover the individual, in this case its YOU because you're giving your daughter a present.
Other examples.. at weddings or in church ceremonies the leader of the ceremony may say 'Dearly beloved.. we are gathered here today.." indicating that everyone here is loved by someone.. friends, family, and as always, God.
In this situation, the subject can be referred to directly by name, 'my beloved xxx' or you can say 'my beloved daughter xxx'. Both sound okay to me.