Yes, Neal, I'm sure as Skybird also wrote. I used to make a trip to Lübeck once, and I'm pretty sure the train embarked the ferry.
I also think it can be a stress day, but then again how many times does one have the option to go to Laboe as someone living far away. I live relatively close, so I'm not sure I will participate in that one-day trip, but if you really wanna go, then do it.
As Skybird suggested, I have visited the homepage for Avis, a rental office. One of many, I have to say. But just as an example.
3 screencaps below.
You'll see on the map that you have about 163 km between Copenhagen Airport (Kastrup Lufthavn) and Rødbyhavn:
And the prizes for vans:
For the 9 person van, more in detail:
That is 2,122 DKK for the rent and the first 100 km. Extra km is 3.60 DKK. And the route in Denmark is ((163+163)-100) = 226 km * 4.50 DKK = 1017 DKK + 2,122 DKK = 3139 DKK. Then you also have the extra km in Germany. But sofar it's 348,78 DKK per person in the van.