Absolutely bring her a gift. Any time you stay with someone in their home, a gift is an appropriate way to show your gratitude for their hospitality.
Since you’re coming to visit her for the weekend directly from a long distance airplane ride, flowers are out of the question. Some thoughtful gifts are perfume or cologne, as you suggested. Stay on the mainstream when choosing since you don’t know her that well. A bottle of Chanel perfume or cologne is something every woman will appreciate. Clothing is probably not a great idea since from your post I’m gathering that you haven’t spent time with her before and may not know her style. Something for her home like a beautiful bowl or vase is a nice idea. If carrying something just won’t work, you can easily order several bottles or half a case, depending on your budget, of nice wine online, to be delivered to her home before you get there. You can also have steaks or seafood ordered and shipped to her home in time for your visit — and offer to cook them for her while you’re visiting!
I hope that helps. Have a great time! 🙂