I am going to be moving 6 hours away within the next few weeks. I have never mov...
The main problem in transporting fish is providing adequate oxygen to them. When shipping fish, the breeders will put them in plastic bags with 1/3 water and 2/3 pure oxygen. As the fish breathe the oxygen dissolved in the water, new oxygen is added from the oxygen sealed in the bag. Air is only about 20% oxygen, so using pure oxygen in the bag will last 5 times longer than just air.
For a trip as short as 6 hours, pure oxygen is not necessary, as long as the fish aren't overcrowded. You could put each fish in its own bag with enough water to comfortably cover the fish, and then add 2-3 times more air as water, and seal the bag. The point of sealing the bag is to keep the water from spilling of course, but also to increase the pressure in the bag, so that the oxygen in the air is more readily dissolved into the water as the fish use up the oxygen in the water.
The bags of fish can then be placed into an ice chest to keep the temperature constant while you travel. The darkness also makes the fish sleep so that their metabolic rate and need for oxygen is reduced. Be sure the water you use in the bag is good for the fish. I recommend preparing the aquarium with water changes prior to traveling so the water quality is good, and then using the water from the aquarium in the shipping bag. You can test the water to be sure it is in the normal range with test strips, or PetSmart stores will test a water sample for you for free. You want to be sure the water is good for the fish, and always use a water conditioner when adding water to your aquarium.
Once you get to your destination, plan on getting the fish out of the bag and into some clean, dechlorinated water as soon as possible. Use an air pump with and air stone in the water to add oxygen, even if you don't have the filter set up. Once you get the whole aquarium set up again, and the filter running, you can add the goldfish back in. The tank will go through the cycling process again, while beneficial bacteria build up to break down fish waste, so you will have to watch the water quality carefully in the new tank over the next 4-6 weeks while it becomes established.
PetSmart offers free guides for setting up aquariums and on water quality changes that occur in new aquariums. Ask for those at your nearest store.