Do it once and see how she reacts because every girl is different. If she says "thanks" and means it and then returns the favour to you in a currency you understand, you keep doing it. If she expects it and does in turn, not act ladylike, then forget it. Chivalry wasn't designed for women (long story), but a feminine woman who can play her role deserves to be treated like a woman. Kinda rare in this day.
Today's woman is independent and she might see you opening the door in a negative light and punish you for doing it in ways you might not easily see. Her actions about it, will define whether or not you will continue to do it. Push and pull on that one.
However, even if you don't do it each time, if you're there first, be a decent human being and do it. But going out of your way....only if she does...as is preens herself up special for a date and so deserves it.