Have you got permission from the car rental company to do this?
Rental companies usually levy significant additional charges, especially if doing a one way drop. The general advice would be to leave the car back, catch a flight to Scotland (or a ferry as a foot passenger) and hire another car on arrival.
Otherwise, I think you will need to wait until you have the car details which I realise is not ideal.
Even assuming the hire company has no problems with you taking a car onto the ferry, is this the most economic way of doing it.
I would call the hire company, tell them what you are doing and find out what type of car they have for you. I'm not sure they allow their cars on the ferry or if they charge more for it.
The answer to your question might be to end your hire in Belfast, take the ferry over as foot passengers (book a through rail-coach ticket from Belfast to Ayr, Glasgow or Edinburgh*, a a Rail-Sail ticket from Belfast to any station in Scotland, as this will save you money) and pick up another hire car in Scotland.
* Edinburgh probably best avoided in mid-August as the world's biggest Arts Festival will be in full swing.
As others have said, I'd be very very surprised if the rental company allows you to take the car on the ferry. Which rental company are you using?
I agree with Wirewiper - much much cheaper to leave your rental car in Belfast and then hire a second rental car when you get to Scotland. Take the ferry as a foot passenger or fly over to Scotland. I also agree that Edinburgh is going to be difficult this month - accommodation is not going to be easy to find, at least not anywhere central. So, maybe base yourselves elsewhere and just drive in to Edinburgh for a day trip.
Why pay to take a car you don't own on the ferry? I presume you have not checked the fares.