It's fine to hang out and travel with friends, but it's wayyyy too easy to only hang out with them, and just drink and relax with only them.
Travel, eat new things, go to new places, meet new people.
I moved to the UK from Australia 7 years ago and while I didn't have a language barrier like you, I think the experiences are similar.
Make sure you get to know locals. Nothing ruins a big OE like staying in the company of other foreigners. Sure, spend time with people from your country if you know any, but don't solely spend time with them.
Use Denmark as a base to see other partd of Europe. If you're already not a huge fan of travelling it will just get harder when you go back to your normal life, and you don't want to regret not travelling years down the line!
Enjoy!!