Moving a 20 gallon tank 20 miles is not a problem. I have moved much bigger tanks MUCH longer distances without loss, several times. (I move a lot for some reason). Start saving up salt buckets now, they are great for moving tank stuff. You can put your pumps and heaters in one, live rock in another, livestock in another, and use a couple to carry tank water.
Just have about ten gallons of new water made up, and siphon out and save as much of your current tank water in clean containers while it is still clean and undisturbed.
Put fish and corals in containers with tank water, remove the rock and put it in a bucket with a lid and a splash of water to stay damp. Make sure the livestock doesn't get chilled. Discard any funky dirty water left over, and I recommend tossing the sand and adding new when you set you if you have a sand bed.
Put all the stuff in your car, drive to new house, set up tank, fill with old reserved water and rock, get your pumps running, make sure temperature is OK and start putting your livestock back in. Use the clean new water you brought to make up for any filthy water you tossed, as well as if you have soft corals I usually toss the water I moved them in as they slime up real bad.
The biggest issue I have when moving a tank to a new place is the livestock getting chilled, or the tank water being too cold when I set up the tank. Purchasing a few of those battery digital thermometers is a wise idea so you can keep an eye on things.