What is the ruling on traveling with a passport that shows the owner's picture without a hijab, given that changing the picture is currently not possible?

Your dislike of men seeing your picture without a hijab is a sign of your faith and modesty, and this is how a Muslim girl should be. Your father should see and appreciate this conscientiousness and not force you to travel, for you are not permitted to enable men to look at your picture unnecessarily. If your father insists on traveling and you cannot avoid it, you may destroy the passport to obtain another one. If this is not possible, then there is no blame upon you for traveling. If the picture was taken before puberty, then the matter is easy.