You'll need to keep the filter material wet and preferably in warm water when you move. Bacteria will die if subjected to below freezing temps or above 110*F. When you move, I would suggest getting a 5 gallon bucket or so to place all your gravel in, put enough water in to just about cover the gravel to keep the bacteria alive, you can also shove your filter media in that instead and then cover the bucket with saran wrap to keep the water inside, or if it's got a lid that's even better.
You'll have to empty your entire tank to move it, never move it with things inside of it, it can have the bottom fall out sometimes and that's no fun to deal with. Ornaments can also go into that bucket. Plants if you've got lives ones can go into a plastic baggie with water to cover them, they will dry up otherwise. Fish can go into plastic-ware food containers for wal-mart or some other place. I like the circle ones with screw on tops, you get a small set of 3 for 1.88 or something like that, pretty good deal I'd say.
Acclimate fish for around 2 hours to fully be sure they get warmed up slowly and get used to the new chemistry. If your pH is extremely different like going from 6.0 to 8.0, you'll need to take around a week, use Spring water which has a pH of 7.0 generally to get them half way, let them stay in a container of that water for a week while you slowly incorporate the new 8.0 pH water until they are acclimated and then into the tank they go.
Your cycle should hold up okay, it might be good to invest in a small bottle of Tetra SafeStart to help the Mini-Cycle that will inevitably happen, that way your cycle can build up again and not hurt your fish.
Wilds: Wajok, Rutilans, Siamentorialis, Hendra
Leopards: Luna, Astrael, Dorian, Cullen, Gallifrey
African Fat Tails: Nox and Lux
Bearded Dragon: Stormfly