Translation:My girlfriend will have bought a watch.
No, in Greek το κορίτσι μου has to be translated as my girlfriend.
There needs to be a lot of context to make κορίτσι/αγόρι + prossessive pronoun into daughter/son but it's rare and the risk of sounding like a total creep is too high, so I suggest keeping these words apart.
Even if a parent of a girl and a boy made a distinction between the two siblings, they would never say 'το κορίτσι/αγόρι μου'. They would either say 'η κόρη μου / ο γιος μου', 'το κορίτσι/αγόρι' (no possessive) or maybe 'το κορίτσι/αγόρι μας' but that last one requires all the context you can get in such a conversation. Same for ~ μου; it's too risky and you need to know how to pull it off. :)
While "my daughter" is a longshot in this case and quite an inaccurate translation, it would be a lie to say that Greek parents don't say "my girl/boy" refering to their children.
I am native Greek and I've been introduced to many people as "my girl" by my parents. And so have many friends of mine.