The fact that you do not want men to see your picture without hijab indicates that Allaah has blessed you with faith and modesty. This is how a Muslim girl should be, keen to observe hijab, cover herself and be chaste. May Allaah increase you in steadfastness and faith.
Your father should understand that you are keen to cover yourself, and he should appreciate that, and not force you to travel now, because you do not have the right to enable men to see your picture unnecessarily. But if he insists and forces you to travel and you cannot stay behind, then you may destroy the passport so that you can apply for another. If that is not possible, then there is no sin on you for travelling with your father.
But if the picture of you was taken before you reached puberty, then the matter is easy, because hijab was not obligatory for you at that time.
And Allaah knows best.