Jumping on this to evangelise about some car ownership alternatives, as it can even be quite the cultural leap even for some Europeans to not own a car.

Firstly Denmark has some brilliant cycling infrastructure I would highly recommend sourcing a bike with a pannier rack to make small trips to the shops easier. If you enjoy it you can always go all in later with a cargo bike and there are many - even from local brands - to choose from (although I have an urban arrow I can also recommend a Bullitt (DK))!

For when you do need a car aside from all the big brands rentals there are also peer-2-peer rentals, eg in Finland I will use go more which is great here and while it looks like they also exist in Denmark your mileage may vary, but I have friends in Sweden who have used this there too.