Ferry to Shetland from Aberdeen

I don't think you can take the car on a ferry. But you can check here:-

To view the CROSS BORDER or FERRY terms and conditions. At STEP2 of our 3 step online booking process, alongside the car photo of your choice, there is a link entitled “IMPORTANT INFORMATION”. Clicking on this link will open an additional smaller window, with the terms and conditions appertaining to that particular car/supplier. Choose then the CAR tab and look under TRAVEL RESTRICTIONS

Try a few different suppliers as each supplier/vehicle type may have a different cross border rule.

But you should be able to rent a car on Shetland , if you wanted.