LIZS - from Glasgow it was 22 hours. There will be a few rest stops, bus limited to 60mph, check in time for the ferry, change of driver, etc. It all adds up and will be about 18 hours.
OP. this isn't ideal, but is do-able.
Try to get a seat with a table. This will give you room for nappy changes.
I agree about lots of little things to keep her amused. Try 1 'gift' to unwrap each hour she is awake (remember she'll sleep for a good part of that journey). Wrap up colouring book, small Disney figures, puzzles, etc. which can be opened and played with on the coach. Take a portable DVD or iPad for watching cartoons (take infant headphones if you can, the coach can be noisy, meaning you'd have to have the volume loud for her to hear, then you'll be annoying other people).
Lots of little favourite snacks too.
Make good use of all rest stops to allow her to run around, and remember that you've got quite a lengthy break on the ferry to look forward to.
Lastly, despite what I say above, try to have as little 'carry on' luggage to ensure that you've got as much space as possible. Overhead storage is small, so you'll end up having bags at your feet making the journey uncomfortable.
Try not to worry about the journey, treat it as an adventure to start off the holiday.
Enjoy yourself!