20 minutes drive is not a problem. here are thing i would do if i were you:
1) get a cooler box, fill with tank water, and put the fish in there.
2) put in there any power head if you have to aerate the cooler;
or run any filter if you can to buy some minutes while draining
3) for canister type filter system, do not drain the system.
4) for HOB type, put some water in bucket and put the unit in.
5) drain the tank to avoid breakage, and load it in a truck or pick up
6) drive away.
7) upon reaching your destination, set up immediately.
8) put up new water in the tank equivalent to the water in a cooler
9) add the water in the cooler and the fish
10) run the system to keep the cycle alive.
11) bingo, you have running tank again...
gradually increase the water until the ideal level was reach...
it may take two days to full the tank but that won't change the logic.
it works like changing the water and keeping the bacteria alive.