She would probably be very offended if you'd ask her father instead of her. What her father thinks is irrelevant, it's her you want to marry, right? Women are not the property of a man, at least not in Sweden. You don't have to ask her father for permission at all, Swedes consider it outdated and patriarchal.
You should know that many Swedes don't get married until they have lived together for years, maybe even have kids together. Some don't get married at all. Of course, there are those who know they've met "the love of their life" and want to get married straight away, but be careful. You might scare her away by making things serious too soon.
How you ask her to marry you? Just make it romantic but simple, and give her a chance of saying "no" if she's not ready for it. She might love you and want to be with you, but not be quite ready to get married yet.
Good Luck!