Stick the old gravel in a media bag or an old panty hose leg on top of the new media, and remove some every week. If you can't move the gravel with you, you're more likely to go through a cycle after the move. Keep everything that you remove from the tank for the move damp so as much of the bacteria as possible survive. Bring your dirty old filter media, and don't be tempted to clean everything while you're taking it down.
If you want to get into planted tanks, another option is to buy a lot of the cheap, weedy, low-light bunch plants. Put those in the aquarium as you're setting it up, and they will absorb the ammonia the same way the bacteria would have. I've sucessfully set up new tanks with large bioloads this way. If you move without the old bacteria and are waiting on the plants, you may need to do a lot of water changes to keep ahead of the cycle.