On move day: I'd look at being out of the house in places he can still relax and stay calm. If you are going to be at the new house then somewhere he can stay safe and contained and be comfy would be best (e.g. a pen with his bedding in it). If you will be in the car then a comfy den using his own bedding, in the boot or similar.
Whatever you pick he's going to have a massive day. Be aware of that - he is likely to get very tired and very tired dogs can look like naughty dogs. They are not, they are just too tired 
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Don't ask him to meet new people on this day, i.e. don't allow them to fuss or focus on him (hard with a cute puppy!) so that he doesn't have that extra pressure, if he finds it worrying.
In terms of the new house: I'd focus on recreating his routine asap and sticking to it. This is going to be ricky as house moves are chaotic, but try and keep meals and walks, playtimes and sleep times the same as at the old house - at least at first. Take plenty of his things with you and try and make sure they are unpacked early (toys, beddings, beds, bowls etc); their familiarity may help him relax a bit.
Be aware that a new house may set back toilet training, so just be prepared to go right back to basics here. Again, in the chaos of moving it can be easy to forget to let the dog out often enough but try not to.
A new house may also set back other training, such as settling alone at night (if you've been doing that), so just be prepared to take a few steps back again.