Sure it can be done, but like everyone else said, it's a lot of work, and planning is the key. If you have access to the place you are moving to, you might want to set up a holding tank there in advance. To speed the filtration process, you can transfer water from your main tank over to your holding tank, and add some live sand, and some live rock. That would be ideal. But if you can't do that, then I would suggest storing as much of your main tank water as possible. you can use simple airation such as air stones, and use a hang on bio-wheel filter for travel to keep the parameters stable. Though I have yet to see any battery powered units, you can buy a small portable generator to supply power to these. You can use those big tupperware containers (some hold up to 50 gal., some more). I would suggest placing your live rock in the containers as well. For livestock, bag them seperatly with plently of oxygen. Your local fish store can fill the bags with o2 for you for a small fee, as they have pressurized o2 tanks. For your live sand, you can either get gallon size zip lock bags, or go to your local fish store, and buy some bigger ones - just don't use any of their old ones, as that is a disaster waiting to happen. They can transfer bad bacteria, and fungus, and no one wants that. Make sure they are new bags. If you use bio bail, or bio balls in your protein skimmer, keep them submerged as to not lose all the beneficial growth on them. You will need that to kick start the new tank. Depending on how long your trip is, you may need to do some water changes. Your fish and any inverts should be fine for up to 48 hours in their bags, however if your trip is going to take longer than that, you may want to consider adding a "store stop" onto your trip. What I mean by this, is that when planning your driving route, scout out a large fish store on your route. Most places can be found on the net, and you can call them in advance to see if they would re-fill the oxygen in your livestock bags. Make sure also to feed your livestock if you have a longer trip, and make a water change to their bags after they eat. Once at your new place, first thing, is to set up your tank (if you weren't able to do it before your move). Add your stored tank water first, then you can use a manual siphon as a funnel to pour in your live sand, so that it wont cloud the water. Give it a few days to cycle, and adjust your lighting accordingly. During this time, I would suggest you move your livestock into a bigger seperate container. Segregate them accordingly, fish with fish, inverts with inverts, and so on. Use some of your stored tank water for the holding containers, and use the "drip method" to re-acclimate the livestock. As long as your parameters have remained relatively stable, you wont need a filter for these temporary homes. Some air stones, and a small heater will suffice short term. I have found that 5 gal. buckets work best. You can get them from Home Depot, Lowes, or any other Home/Garden place. After a few days of cycling your main tank, check the parameters, and if stable, use clear tubing to create a siphon (stick one end into your tank, and secure it, and then suck on the other end to create a vacuum effect). Just make sure you take your mouth off before the water gets to your end -- NASTY. Tie a loose knot on the bottom ends that go into the holding buckets, and tighten them slowly to create a slow drip into them. This may take a few hours, as you need to at least double the water volume in the buckets. Monitor your lifestock for any erratic behavior, but also note, that some may naturally lie on their side, and appear sluggish at first - this is fine. But if their breathing becomes strained, or exceedingly fast, stop the drip to that bucket, check the water quality, and allow the fish to regain their composure before resuming. Once all are acclimated, you can move them to your main tank, and continue to monitor them, and your water quality. A good way to check vitality, is to offer food soon after acclimation.
Hope this helped some!
--Emi