We have a very helpful article on
vehicle rental that you may be interested in. It has lots of useful information and a link to rental car companies that you may wish to contact. Please keep in mind the need to have an office at the Belfast port to drop off your car before sailing over to Scotland.
As Visit Belfast mentioned, please check with the terms and conditions of the many rental companies about oneway rental and also the requirement about informing them of crossing the border for insurance purposes.
Also, the ferry port in Belfast has the service provider
Stena Line who you will need to contact regarding a crossing and times.
It is also possible to find tour operators who can help you with your trip. We have a list of
tour operators some of which can offer self-drive options which may be a good idea, although I'm sure you will be able to sort it out before you come over next June!
I hope this helps and you can turn your focus onto your itinerary while here on the island of Ireland.