I had to do a massive relocate (UK/Ireland) with my elderly, timid cat and was dreading it, but with the help of a cat-friendly vet it went really well.
The advice which was helpful was NOT to use a massive carrier as cats tend to feel less stressed when they are in a 'safe' contained space. I used a carrier which was only slightly bigger than the one I use for vet visits etc - enough for the cat to turn round, lie down, stretch etc. I used a clip-on water bowl about half full and it didn't spill.
Otherwise - yes to PPs suggestion to use Zylkene. It did make a difference - just sprinkle it on the cat's normal food for a couple of weeks before, and during, travel I also used Felispray on the cat's bedding.
The cat traveled really well - no incidents - and that included an overnight stop at a hotel. Two days of travel. I know you're not doing an overnighter but for anyone else, I'd recommend using disposable litter trays. You just chuck the whole lot in the bin as soon as it's dirty. Saves a lot of hassle, especially if staying in a hotel.
The other thing I did was put the cat in a really nice cattery for a couple of days prior to the move. We then picked her up on the way. Apparently moving day is a very common time for cats to get distressed and run off/out through an open door.
Good luck - I'm sure I was waaaay more frightened than the cat on the day, but it was all fine. Hope your move goes well. And do talk to you vet.