Three years is little difference when people are done with their degrees. Initially, three years is possibly a whole tier of schooling, but later in life in doesn’t matter at all. In fact, it’s probably preferable.
In my country, there was a whole theory about girls maturing 3 years ahead of boys on all levels, the result being minimal age for marriage at 18 for women and 21 for men. That law is no longer there. The whole thing was probably propaganda helping to deal with the needs of military draft. Anyway, it’s normal for a guy to be older.
Now, yeah, you’ve got to consider that she isn’t legally adult and parents have a lot of responsibility in her life. I don’t think it would be seen as necessary where I live, but in a conservative Anglo-Saxon community, it probably would, AND it could be helpful in convincing a Catholic father that it’s no scheme or predation but just an accident of life, a situation that was normal a couple of decades ago anyway, and you have no ill intentions. HOWEVER, that doesn’t mean that parents are entitled to plan out her daughter’s dates.
Now the obvious result of your telling her father is that you’re assumed to be seriously interested and you have to live up to your declarations. Something of that kind could be rather constricting. You will need to know when to do that. It might be necessary to explain to the father that you’re telling him and letting him know because of the special circumstances, not because you’re about to ask her hand some time soon.
Speaking of, people were right when they told you that dating is for the purpose of finding a partner for marriage. I don’t think that means all teenage crushes should be banned, but there’s a lot of wisdom in not “pairing up” until such time that one’s fully developed and won’t change so easily, until one has a job and a stable situation and so on. That’s what I would suggest when it comes to looking for a date on purpose. On the other hand, things are different when the date comes to you.
My advice would be to give yourself time and see what happens. See if you haven’t changed your mind in, say, two weeks from the moment you experienced so intense emotions. See if you still think she’s interested, if you still think you are etc.
And obviously, you don’t go talk to her dad just like that. You can go and a pay a visit to him specifically when both you and the girl decide it’s a good idea to start dating, or you can use the opportunity when you’re visiting her in her house and talk to her father even before she knows (“Well, sir, I haven’t told her yet, but I will have to soon and I would feel better if you knew, given that she’s not legally adult yet and I am. Thus I would like you to know first and would like to know what you would have to say about it.”). Keep it short, polite and as light-hearted as possible. As I said, you aren’t asking to marry her.