I rent a car, but from Dexxter I must register it in the system. It asks me to fill in details such as CO₂ emissions, purchase date and registration date. Since I did not purchase the car, is it correct to fill in that information? Or should I approach this in a other way?
You will indeed have to fill in that information, even for a rented car :) This is to ensure that the car tax system runs good.
If you do not have any details, you will need to create an unknown car. See also the learning center if you search for 'unknown car'.
You really should try it out for yourself. Even if you don’t have a company number yet, you can already go ahead.
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