You only have the one little guy who is still a kitten so I bet he will do great. Here is my long snoring reply, having moved multiple times with multiple cats
It's stressful every time but they have been great about it. No matter what you do, they will most likely be nervous and shy, even hide in their new home. Let them come around at their own pace. But you can greatly reduce their stress~~again, my advice is more with older, multiple cats, but you may find something uselful in my rambling!!!
When you are moving, isolate cat/s in one room that is already emptied (aside from their needs) or move what is in that room last. They should not be in the immediate vicinity of all the ruckus. Plus they could scatter about and get lost or hurt.
Keep their favorite bedding (even a tshirt of yours with your scent) with them as you are packing trucks, and use that bedding in their carriers. Spray the carrier with Feliway about 20 min before placing kitty in carrier. You can also spray the car a bit for good measure. Oh and try to avoid feeding the cats too close to the move--at least 2 hours prior is fair.
Some cats will like a towel draped over the carrier for a sense of security.
Make sure the carrier is WITH you in your traveling vehicle and stable.
At the new house, I always try to set up something ahead of time (a temporary holding room with their litter boxes, etc.) This move I am plugging in Feliway diffusers in rooms at least a week ahead of time.
THen I place cats in a quiet room, door shut, with their carriers door open. Water right away, food a little later (in case of upset tummy). Litter is available, bedding is already in carrier or I place something familiar.
Cats stay in that room while we move furniture in--that room is used last. I don't let cats out till most of the ruckus is over, and usually much later, sometimes the next day--depends on set up of the house. I like to start with one section at a time if possible--not just open them up to the entire place (if it's a large home).
I can always expect some hissing and hiding from most of my cats--(one of my females loves to move--she is character). I show them where their litter boxes are--but this should be done after they are more comfy in their holding room and not still hunkered down in their carriers.
Then they have to explore at their own pace. Do a good 'cat proofing' of a new home--things *THEY* could get into but you wouldnt necessarily think of. I had 2 cats hide behind DRY WALL in the basement. We couldnt; find them for hours and I was in tears. There they were, looking up at me, all wide eyes and 'hey mom!'. We have *NO* idea how they got there and we had to rip the board down to get them out.
Ideally, if you can move your stuff into your new place THEN bring your cats after your mostly moved in -- that would work best. We might be doing that this time, (time and distance is key here).
Pets are more resiliant than we give them credit for. Be patient with them and they will come around