You will have a fabulous time in Copenhagen, Heart Star! I really love it there. I find the Danish people to be very friendly, in general (not in an "effusive" American way, but still very awesome ).
If you have time, a great place to visit (for free) is the botanical gardens. Spectacular. One of my favorite shops, along the way to Nyhavn, is Superlove. Very cute housewares, and some great Danish clothing brands, too. http://www.superlove.dk/
As for fashion tips, you will be perfect in your dresses and cardis. Possibly you might want to wear tights. Depending on where you are coming from you may already be acclimated to the weather. The Danes love scarves, and if you were going to buy any item of clothing there, that might be something you could stock up on. I do recommend flat shoes. Lots, and lots of cobblestone streets. Same goes for Malmo, Sweden.
Thank you so much for all the suggestions/advice nori west. I've already been on the super love website
I'm really looking forward to the trip!