Well done on taking the big step! Feels a little daunting doesn't it. :)
My son was 11 weeks old when we had our first trip away (6 hour train ride) and I had sleepless nights before it worrying about it but turns out I was worrying over nothing. I was worried he'd be unsettled and cry etc etc.
Main thing is try to relax as much as possible about the whole thing or your little one will pick up on your anxiety and be more restless.
Remember, at this age baby will still sleep for periods of time so try to coincide this with part of your journey, either the beginning or the end. Babies tend to like car journeys as the motion soothes them to sleep. Feed baby before you go and get LO all comfy.
Sing and talk whilst you are driving if baby gets irritable and if all else fails just remember that although the journey takes 3 hours it doesn't mean it has to be, you can take a little longer. What I mean is if baby really needs a cuddle then pull over for a bit. Perhaps even schedule in a stop or two along the way.
In a few months, when you're planning your next tip you'll wonder why you were ever worried. I'm currently planning another 6 hour train ride with my son who's now 9 months old and crawling.....eeek!
Good luck and enjoy your break.
Indigo
xxx