While this may seem like just another thing that’s added to your plate, make copies of all of the keys prior to you move. In all of the chaos of the move it would be easy to misplace a key, and that is the last thing you want to deal with on your moving day.
A majority people move the months of May and September. This is because May and September are warmer, which makes moving easier.
Be sure to choose a date that makes sense for you. You don't want to cause yourself stress unnecessarily.