First, congrats on the job to him! :)
As for your furbaby, 4 hours in a car will fly by. I've moved my two cats probably 6 times in the past 5 years. 3 of them were 4 hour trips (moving them to/from school at the end of the semester/year) and the other 3 were long distance moves, 2 with hotel/overnight stays in other places. I bought scraps of fleece for their carriers to use as blankets - get extra just in case it gets dirty/smelly.
One of the best things I've done is take away their food about an hour before we leave. I know it seems mean, but my "oldest" WILL throw up within 15 minutes of being in the car. (I've tried driving around for 20 minutes before I leave... and she doesn't barf then.) Take away the food, and she's good to go. I let them have water. During rest stops (as long as the weather outside is ok) I let them out of their crates, put water out, and pull out the litter box, just in case. Then I'll take a nap or get a quick snack, and hang out in the car with them.
For the new place-take a blanket that your cat regularly sleeps on and pack it-unwashed-and then bring it out in the new place and set it up in a corner away from a lot of traffic so she can get used to the space on her own. Put out some of her favorite toys and create a "safe" space for her where no one can bug her.
As far as the harness goes, one of my cats LOVES it, the other one would basically (based on her reactions) die than ever be put in one ever again. So, it's worth a shot. Just make sure you get one that she can't pull herself out of. Cars and dogs and strangers and who knows what else may startle her, and she'll try to pull out of it. I wouldn't recommend trying out the harness for the first time while moving her for the first time, though. Lots of stress at once may not be the best for her. If you decide to get her a harness, put her in it for 10 minutes and love on her. Let her know it's okay and give her treats. Do this for a while, adding time onto the "harness sessions" don't attach a leash-and make sure you're watching her the whole time. She'll get used to it eventually and then take her outside gradually. New things are terrifying for some kittens.
(This is all from my experience as a cat-owner. I grew up with cats (have had 4 throughout my childhood) have two of my own and I have 2 "nephews" and 1 "niece" .) Feel free to message me if you have any cat questions!