While I was out on my morning run happened to think of a few more things you may want to keep in mind:
If you drive across the bridge to Malmö in the morning, you'll probably be ready to leave Malmö by mid afternoon or so. You'd get a quite different camping experience if you drive to Falsterbo, at the extreme southwestern tip of Sweden. Just under half an hour by car from Malmö. Easy to find: head south out of Malmö and after you cross the little bridge across Falsterbo Kanal (can't miss it!), you'll be driving through a nice wooded area for about a mile, and after that you will have a large open nature reserve on your left ("Ljungen") for two miles or so. After that you get to a traffic circle. Go left. After about a mile, the camping will be on your left. It's right on the water, with a unique white sandy beach. Google "Ljungens Camping Falsterbo" for more info. Falsterbo is a very small town (less than 1000 people year round), that really "wakes up" during the summer, with many people spending just the summer there. I lived there for four years, long time ago.
Then, the next day, you can simply follow the coast (most of the time), heading east through Trelleborg, to Ystad. You'll probably find that a few hours in Ystad will be sufficient, and if you want to see more places of interest after that, continue in an easterly direction. Kåseberga is a short distance beyond Ystad, and there's a remarkable stone setting in a ship formation (from the Viking period), called Ales Stenar (The Stones of Ale). Google it for more info, or preferably, buy a good map of Skåne. From there, continue around the southeastern tip, up to the town of Simrishamn. Another nice little town, right on the water. From there, you can then head straight back to Malmö, about an hour away.
And, just a few more things about Copenhagen: when you're walking along Strøget, the pedestrian street, make a quick detour to Runde tårn ("Round tower"), which is an old building from the 17th century. You can walk up to the top (there are no stairs, you walk up on a ramp!), and you have a nice view from up there. If you're walking from Rådhuspladsen towards Kongens Nytorv, you will make a left onto Købmagergade. On the corner is Illum, a large department store. Walk on Købmagergade for a few blocks and Runde tårn will be on your right. Then, when you get back to Strøget, and continue to Kongens Nytorv, you could cross the large square and keep to your right. That will take you to Nyhavn (New harbor), right on the other side of Kongens Nytorv. Nyhamn used to be a real seedy place, frequented by sailors, but it has been cleaned up over the last 10-20 years and is now a popular tourist spot. If the weather is nice, you're going to see plenty of sidewalk cafés, where people will be enjoying a beer or a cup of coffee and a delicious "danish". Except they are not called "danish" in Scandinavia - they are called "wienerbrød" (=Vienna bread!).
Incidentally, "The little Mermaid" statue is a couple of miles north of here, out by the harbor.