Certainly don't miss out Skagen!
From Struer drive west through Lemvig and head north through Thyborøn (crossing the place, where the 'Limfjord' meets the see (Vesterhavet). Then continue further north 'till you reach Skagen.
From there you could take the 'motorway' south through Aalborg to Århus - which is definitely worth a couple of days. Take a walk through the older part of the city (called 'Latinerkvarteret'). There you find the best cafées and small shops.
By the way - you will find 2 B&O shops there, not far from each other. Be sure to visit the art museum (called Aros) and take a walk high-up along the many-coloured glass gangway. If you are interested, do visit 'Den gamle by' - the museum with old buildings from all parts of Denmark. There you can also find a (newly opened) street with houses and homes from the sixties - including a 'radio and tv shop' like they were 50 years ago.
If your plans (and your time) allows for it - do visit the old town Ribe (drive west to Esbjerg and then south) and drive further south/west to see the 'Vadehavet' by Højer. That is a part of the countryside, where you can experience the influences of 'ebb and flow'.
If Hans Christian Andersen is of any interest, stop by in Odense, when you head east for Copenhagen. Nice city - worth visiting.
Don't use your (hired) car in Copenhagen - walk or use the bus! Lots of things to see and visit in the capital of Denmark!!!
If you want to make a short visit to Sweden too, go north from Copenhagen, stop by at Helsingør (visit the castle) and go by ferry to Hälsingborg (a very short trip). From there go south to Malmö, and take the long bridge to Copenhagen.
You will be very close to the Airport (Kastrup) after arriving in Denmark again.
This might help you explore Denmark - I hope!
Have a safe journey 🙂