I moved 200 fish and three large aquaria and yes it can be done.
Don't wash/rinse the substrate; bag it (use those fish bags, double for extra strength) and as it is wet some of the bacteria will survive. Of course, it depends upon the length of time, they can't go long without oxygen which they obtain from the water passing over them.
When you set up the aquarium condition the water very well [don't skimp on the water conditioner]; if the ph is above 7 (as I believe someone said it is in Florida?) use an ammonia-detoxifying conditioner. [If the water is below 7, slightly acidic, the ammonia converts to ammonium which is harmless so this won't be a problem.] Dose the tank with "Cycle" or "Stress Zyme" which are biological supplements that immediately add the bacteria to start the nitrogen cycle and they significantly reduce stress on the fish.
Float the bags of fish in the water, slowly add water from the tank to the bags over a period of time to get the fish adjusted. Not only temp, but more importantly is the pH and hardness which may be different and if the pH is different by more than a few decimal points (say .2 to .6) this must be done slowly. When ready, net the fish out of the bags into the aquarium; do not pour the water in. With new fish from a store, this is to prevent releasing pathogens and whatever else into your tanks (even the quarantine). In your case, it is to keep the excess ammonia (and the bags will be full of it depending upon the length of time) out of your new tank to further assist the cycling and ease the stress on the fish.
I moved more than 200 fish this way, and did not lose one in the new tanks.
[By the time I posted this, I see Arkamaic has already covered some of it, so no intention of restating. B.]
Last edited by Byron; 06-15-2009 at 11:49 AM..