I have tried to use the following website to reserve passage for an auto and 4 passengers from Faaborg to Soby (on the north tip of Aero). The reservation page is in Danish. It looks like they want the auto registration number, but I am renting. Anyone reserved in advance with a rental car?
I went to Aero 7 years ago at the end of May. We didn't reserve a space for us or our car. It wasn't a problem. Things could have changed, but that was our experience.
Try to call them at +45 62 52 40 00 and ask what the practice is for rental cars.
It should be possible to find someone on the phone who speaks english.