In this small of a system, get the new tank setup. Purchase new sand, not the live bagged stuff just the dry stuff and rinse it well to get all of the powder out of it. Take about 1/2 of the water from the existing tank and put it into the new tank. Take the rock from the old tank and place into the new trying to get the scape you want although no matter what you do you will probably rearrange it later. Then put the new sand in around the rock work filling in all of the areas where they can be under the rock. Use a piece of PVC tube with a large funnel on the end that you can dump the sand into and direct it where you want to from the other end, If you work slowly and keep the end of the PVC in the tank close to the floor of the tank you will minimize any sandstorm.
So now you have an old tank with some water, sand and coral in it. A new tank with some water sand and rock in it. Take a cup or two of the old sand from your tank and add it to your new tank. Fill the new tank with newly mixed, temperature adjusted saltwater. Then go ahead and move you coral. You will be good to go. You should get minimal if any ammonia spike this way, and whatever you do get your bio filter should be able to handle.
JMO